Detroit’s Javier Baez hits a two-run home run against the Boston Red Sox in the eighth inning Monday in Detroit. Paul Sancya/Associated Press

DETROIT — Javier Báez smashed a pitch over the fence and made a slick play in the field.

When the Detroit Tigers signed the two-time All-Star shortstop to a $140 million, six-year contact last winter, they were banking on him having a lot of games just like that.

Baez hit a tie-breaking two-run homer in the eighth inning and made a diving stop and throw from one knee for an out in the second, leading Detroit to a 3-1 win over the Boston Red Sox on Monday night.

“Javy made a big-time play at shortstop and got a hit we needed,” said Miguel Cabrera, who had a sacrifice fly and two hits to pull within nine of the 3,000th of his career. “It was a big game for us after losing two to the White Sox.”

Baez sent a 396-foot shot to left off Ryan Brasier that scored Austin Meadows, bringing home two players who are part of a new-look team that is hoping to contend.

Michael Fulmer (1-0) pitched the eighth and Gregory Soto closed the game for Detroit’s first save of the season.

Austin Davis (0-1) took the loss after giving up one run and two hits in one inning.

Boston led by multiple runs in each of its first three games against the New York Yankees, but didn’t win until Sunday when Bobby Dalbec hit a tie-breaking solo homer in the sixth inning.

The Tigers were behind by two-plus runs in all three games against the Chicago White Sox, and rallied only in the opener on Báez RBI single in the ninth that scored Matthews in their Detroit debut.

“If you’re looking for panic, you should look somewhere else,” Manager A.J. Hinch said.

The Tigers flipped the script against the Red Sox by taking a 1-0 lead in the first inning on Cabrera’s sacrifice, but didn’t generate much more offense until late in the game.

Detroit’s Matt Manning was perfect through four innings, before J.D. Martinez led off the fifth with a solo homer to pull Boston into a 1-all tie.

Manning, the No. 9 overall pick in 2016, gave up only Martinez’s solo homer over six innings.

“He had some good stuff early on and he kept us off balance and was giving us trouble,” Martinez said.

Alex Lange and Fulmer each gave up a hit in one inning of scoreless relief. Soto, too, allowed only one hit.

In his Red Sox debut, Michael Wacha got off to a shaky start before shutting Detroit down. Wacha loaded the bases in the first with one out on Meadows’ single and two walks, but got out of the jam by giving up only one run on Cabrera’s sacrifice fly.

“That first inning was kind of frustrating for me,” Wacha said. “Giving a couple free passes there ended up leading to a run, but I felt like I settled in pretty well after that.”

Cabrera doubled in the sixth, giving him 1,117 extra-base hits, pulling him into a 19th-place tie with Hall of Famers Ted Williams and Jimmie Foxx. Hall of Famer George Brett (1,119) and Manny Ramírez (1,122) are the next two on the all-time extra-base hit list.

Later in the game, Cabrera singled for the 2,991st hit of his career.

NOTES: The Red Sox are averaging just three runs a game. “I don’t want to say any excuses, but we’re still three weeks behind a normal buildup,” Martinez said. … Trevor Story missed his second straight game with flu-like symptoms. Manager Alex Cora reiterated that the team’s new $140 million second baseman does not have COVID-19, adding Story arrived in Detroit. “He feels weak,” Cora said. “Hopefully he can come here (Tuesday), get him moving around. I’m not sure if he’s going to play (Tuesday). We’re trying to shoot for the last day of the series.”… RHP Matt Barnes pitched one inning after being out with a tight back.