ST. PETERSBURG, Fla. -- The Tampa Bay Rays' formula that has them holding onto first place in the American League East worked to perfection on Saturday against the Boston Red Sox.

Rays starter Matt Andriese gave up one hit and struck out five batters over six innings, closer Brad Boxberger got his 20th save of the season and Jake Elmore hit a two-run home run to lift the Rays to a 4-1 victory at Tropicana Field.

Andriese (3-3) needed only 70 pitches (48 strikes) to get through six innings before handing the game over to the Rays bullpen. He easily could have went another inning, but Rays manager Kevin Cash has been sticking with what's worked for his team all season.

"That's kind of been our M.O. the whole season, especially when we get the lead," Cash said about leaving Andriese in the game. "It just kind of worked out perfectly today."

First baseman Elmore broke open a scoreless tie in the bottom of the fifth when he roped a home run barely inside the foul pole in left field off Red Sox starter Wade Miley to give the Rays (42-33) a 2-0 lead.

"(He hit) a slider that I was trying to bounce and I left it up," Miley said. "I thought I had him in a pretty good situation, but I didn't execute the pitch and he did a good job with it."

Shortstop Asdrubal Cabrera led off the inning with a triple.

"In that situation my goal is to drive the ball to the outfield so we can get the run home," Elmore said. "I didn't even think home run, all I thought was, 'Please stay fair,' because I knew it was at least getting down. I thought I kept it fair and thankfully I did."

Rays catcher Rene Rivera added a solo home run over the left field outfield bleachers off Red Sox reliever Matt Barnes in seventh to give the Rays a 3-0 lead.

Boston (33-43) did not have much success against Rays pitching and mustered only three hits, one of which was a solo home run by left fielder Alejandro De Aza in the eighth inning off of reliever Kevin Jepsen.

"It's the way we do things here," Andriese said about leaving after six innings. "We have a lot of trust in our bullpen, the big three back there.

"Got a lot of confidence in those guys. If we can get out of there with a win that's all that matters."

Rays third baseman Evan Longoria gave the Rays an insurance run in the bottom of the eighth with a solo shot to observation deck in left center off Barnes, who was called up today from Triple-A Pawtucket and didn't arrive at the ball park until around noon.

"I felt like I threw the ball well ... ," Barnes said. "I made two mistakes and those two mistakes happened to be home runs. It's frustrating but it's part of the game sometimes."

Miley (7-7) went 6 1/3 innings and gave up two runs and five hits while striking out eight on 106 pitches (65 strikes).

"I thought Wade pitched very well," Red Sox manager John Farrell said. "You know, he gets in a 1-2 count to Elmore that the slider doesn't get to the intended spot for the two-run homer.

"But even when he had men on, he made big pitches. He got a couple of key ground ball double plays early in the game."

NOTES: Rays RHP Jake Odorizzi had a 51-pitch batting practice session before Saturday's game and said he will make one rehab start with Class A Charlotte next week before rejoining the rotation. ... Red Sox SS Hanley Ramirez (hand) probably will be given three or four more days before the team decides whether he will go on the 15-day disabled list. ... Rays RHP Matt Moore was to start the first half of a doubleheader with Triple-A Durham on Saturday after his scheduled start Friday was pushed back because of rain. He is expected to make his first major-league start since April 7, 2014, on Thursday against the Cleveland Indians. ... Red Sox C Ryan Hanigan was to make a rehab appearance for Double-A Portland on Saturday and was expected to catch all nine innings.