KANSAS CITY, Mo. — Alex Cora kept watching the Red Sox hammer pitches right at the Kansas City Royals during the first few innings Tuesday night, and the Boston skipper was confident that eventually some of them would find their way through.

Eduardo Nunez finally solved the problem by depositing a pitch over the fence.

His pinch-hit, three-run homer in the eighth inning broke open what had been a nip-and-tuck game, and the Red Sox went on to beat the Royals 8-3 to open a grueling stretch of 17 games in 16 days.

“We were swinging the bat well. I know we didn’t score early, but that was the hardest we’d hit the ball all season,” Cora said. “Eventually we got some results.”

Rafael Devers also drove in a pair of runs for the Red Sox, while Eduardo Rodriguez (6-3) kept the Royals at bay over 5 2/3 innings. He allowed just six hits while striking out seven, his only mistake a pitch in the second that Cheslor Cuthbert sent to left field for a two-run homer.

Glenn Sparkman matched Rodriguez most of the way, but he left a runner on base when he was lifted with one out in the sixth. Scott Barlow (1-2) promptly gave up the lead with a miserable relief outing, and Nunez’s homer off Jake Diekman in the eighth inning was merely the finishing touch.

The Red Sox improved to 9-1 in Rodriguez’s last 10 starts.

“I think the only pitch I missed was the one that he hit the homer,” Rodriguez said. “Everybody believes in this offense. We’ve just got to keep the game close when we’re out there.”

Meanwhile, the woebegone Royals lost for an AL-leading 20th time when they had the lead.

Even more frustrating for Kansas City: Sparkman was slicing up Boston’s lineup, allowing just two hits through five innings. But after Mookie Betts’ leadoff double in the sixth, and Andrew Benintendi’s flyout, Sparkman was yanked by manager Ned Yost despite having thrown just 80 pitches.

“I felt really good,” Sparkman said, “but I hadn’t gone that high, so 85 was probably the limit.”

Barlow entered the game and the spark went out of the Royals.

J.D. Martinez delivered an RBI triple, Devers drew a walk and Xander Bogaerts added a sacrifice fly to knot the game 2-all. Brock Holt followed with a double to give the Red Sox their first lead.

“Cuthbert’s home run was good. We took a two-run lead going to the sixth there,” Yost said. “Sparkman’s high-water mark was 68 pitches, so we were going to take him to 80 or around there. He got right to the 80 mark. We decided to bring in one of our most productive relievers.”

It was still 3-2 in the eighth when Nunez connected for Boston’s second pinch-hit homer this season.

“It was a matter of having good at-bats,” Cora said, “and getting to the bullpen.”

TRAINER’S ROOM

Red Sox 1B Mitch Moreland (low back strain) hit off a tee and could return when he’s eligible this week, Cora said. He went on the injured list retroactive to May 26. … 1B Steve Pearce (low back strain) is still not doing any baseball activities. He went on the IL on Saturday.

Royals 3B Hunter Dozier (strained oblique) was placed on the IL before the game, though the move was retroactive to last Friday. Yost was optimistic Dozier will be back in about a week.

DRAFT UPDATE

The Red Sox made a couple of convenient picks when the first-year player draft resumed Tuesday. In the third round, they selected big Kansas right-hander Ryan Zeferjahn. Two rounds later, they took his battery mate in catcher Jaxx Groshans.

The Royals focused on college pitching on Day 2 of the draft, grabbing five more to go with right-hander Alec Marsh, their compensatory pick out of Arizona State. The Royals likewise stockpiled college arms in last year’s draft, using their first five picks on them.

UP NEXT

Left-hander Chris Sale (1-7, 4.35 ERA) tries to bounce back from three straight shaky starts when he takes the mound for Boston on Wednesday night. RHP Jakob Junis (4-5, 5.35) starts for Kansas City.

— Associated Press —

KANSAS CITY – As expected, the Royals used their No. 2 pick in the Draft to select Texas high school shortstop Bobby Witt Jr., the son of former Major League pitcher Bobby Witt.

Witt, from Colleyville, Texas, hit .489 this year with more home runs (15) than strikeouts (11).

General manager Dayton Moore said in a conference call that the Royals scouted Witt for virtually every inning he played during his senior year. Moore also said he spent two days with Witt and his family about a month ago.

“Very impressed with his makeup,” Moore said.

Witt said that he and his father teared up after the Royals made the pick.

“It was emotional,” Witt said in a conference call. “This is something I’ve dreamed about. I’m super-excited. I’m at a loss for words right now.”

The only other times the Royals had the No. 2 pick, they chose Alex Gordon (2005) and Mike Moustakas (2007).

Witt, 18, is six feet and 180 pounds, and was ranked the No. 2 overall Draft prospect by MLB Pipeline. He was the Gatorade 2019 national high school player of the year.

“Alex Rodriguez is the best shortstop prospect I’ve seen, but Bobby Witt Jr. certainly belongs right up there,” a longtime scout, now with a NL club, recently told MLB Pipeline. “He can match up with guys toolswise, and what he also has is a high baseball IQ. People lose sight of it because the tools are so strong, but he’s a really good player to go with it.”

The Royals also view Witt as a versatile player who could be moved around defensively, perhaps even to the outfield. The Royals have budding star Adalberto Mondesi at shortstop, Nicky Lopez at second base and Hunter Dozier at third base for the foreseeable future.

“I feel like I can play any position they want me to play,” Witt said. “That’s up to them.”

“He is a very versatile player, no doubt,” Moore said.

As the No. 2 pick, Witt’s assigned slot value will be $7,789,900.

The Draft continues on Tuesday with Rounds 3-10.

— Jeffrey Flanagan MLB.com —

Royals third baseman Hunter Dozier, who is leading the Kansas City with a .314 batting average, went on the 10-day injured list Monday due to a chest injury.

The move was retroactive to Friday. Dozier hasn’t played since leaving Thursday’s game with what was described by the team as “right-sided thorax tightness.”

The 27-year-old Dozier is having a breakout season after hitting .229 with 11 home runs in 101 games last season.

In addition to batting average, he leads the Royals in on-base percentage (.398) and slugging percentage (.589), and he ranks second in home runs with 11 in 52 games.

The Royals open a nine-game homestand Tuesday, when the Boston Red Sox visit to begin a three-game series.

— Field Level Media —s

ARLINGTON, Texas — Adrian Sampson struck out a career-high 11 in seven innings and earned his first major league win as a starter, leading the Texas Rangers over the Kansas City Royals 5-1 Sunday.

Texas won three of four in the series. The Royals ended a 1-6 trip that left them with a major league-worst 8-23 road record.

Sampson (4-3) posted his previous three victories in relief of an opener. He gave up one run and eight hits, and walked none.

Texas reliever Jesse Chavez pitched a scoreless ninth to run his shutout streak to 18 1/3 innings.

Brad Keller (3-7) allowed three runs in seven innings. The American League leader in walks with 42 didn’t walk anyone but had two wild pitches, one that scored a run.

Texas took a 1-0 lead in the third on three opposite-field singles and added two runs in the fifth, the second on an opposite-field single by Nomar Mazara.

Sampson escaped a jam in the fifth in which the Royals used bunt singles by Terrance Gore and Billy Hamilton to load the bases with none out. He retired Whit Merrifield on a liner, Adalberto Mondesi on a swinging third strike and Alex Gordon on a called third strike.

Jorge Soler hit his career-high 15th home run in the sixth inning for Kansas City’s run.

The Royals loaded the bases in the eighth inning with two outs, but Shelby Miller got Cam Gallagher to fly out to center field.

GALLO TO IL

Rangers CF Joey Gallo, who’s tied with three others for second place in the AL with 17 home runs, was placed on the 10-day injured list with a left oblique strain that happened in Saturday’s game and will probably miss about two weeks.

“Hopefully it’s going to be a quick trip,” he said.

SHORT HOPS

Texas scored a second run on a third wild pitch, in the eighth inning by Jake Diekman. … Mondesi hit his major league-leading eighth triple, breaking a tie with Merrifield. . Royals 3B Cheslor Cuthbert had his second career three-hit game.

TRAINER’S ROOM

Royals: C Martin Maldonado, who left Saturday’s game in the sixth inning with right forearm tightness, was available but given the day off.

UP NEXT

Royals: RHP Glenn Sparkman (1-1, 4.21) will open a home series against the Boston Red Sox on Tuesday. His previous start lasted two batters into the second inning, when he was ejected for hitting the Chicago White Sox’s Tim Anderson.

Rangers: LHP Drew Smyly (1-3, 6.98) will start Tuesday’s series opener at home against the Baltimore Orioles on five days’ rest unless manager Chris Woodard decides to move up LHP Mike Minor (5-4, 2.74).

— Associated Press —