ST. PETERSBURG, Fla. — The Boston Red Sox are creeping into playoff contention, and the Tampa Bay Rays didn’t have the pitching depth to give them a full fight Monday night.

The defending World Series champions pulled within a game of Tampa Bay for third place in the AL wild card standings with a 9-4 victory over the Rays, who finished with a position player on the mound despite trailing by only five runs entering the ninth inning.

J.D. Martinez hit a three-run homer to help the Red Sox build an 8-0 lead that Tampa Bay trimmed with three runs in the eighth off Nathan Eovaldi, who returned from a three-month stint on the injured list to pitch for the first time since April 17.

Martinez added an RBI double in the ninth after Rays manager Kevin Cash decided to send rookie infielder Mike Brosseau to the mound instead of using a fourth reliever out of what Cash described as an overtaxed bullpen that wasn’t helped by Tampa Bay getting just 2 1/3 innings out starter Jalen Beeks.

The manager said if his team had been able to trim its deficit to four, he would have used reliever Diego Castillo, who had been warming up.

“It’s a tough decision. Basically, the grand slam, four runs (behind) was the mark. So, if we got to 8-4, Diego was going to come in the game,” Cash said. “We went into the game knowing our pitching had been fairly taxed.”

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Major League Baseball and the players union agreed in March on a rule change for 2020 prohibiting position players from pitching through the ninth inning unless the player’s team is winning or losing by six or more runs.

Brosseau, who started the game at second base, allowed doubles to Xander Bogaerts and Martinez. He was the fifth player to pitch for the Rays in the game.

“Cash kind of asked me there in the eighth inning if I’ve ever pitched before,” said Brosseau, the second position player Tampa Bay has used as a pitcher this season. “I told him I have, twice in low-A. He just asked me to throw strikes and hopefully get outs. I told him I was up for the challenge.”

Eduardo Rodriguez (12-4) allowed two hits over seven scoreless innings to win his sixth straight decision. He limited the sputtering Rays to a pair of infield singles and four walks before being replaced by Eovaldi.

Eovaldi, who had surgery to remove a loose body in his right elbow, labored through two-thirds of an inning, losing the shutout on Travis d’Arnaud’s RBI double. Austin Meadows also doubled home a run, and Yandy Diaz added an RBI single off the right-hander.

Martinez, Andrew Benintendi and Sam Travis homered in the third inning, when the Red Sox scored seven runs against Beeks (5-1), a former Boston prospect who lost for the first time since being sent to the Rays in a trade for Eovaldi last summer. Martinez’s three-run blast was the biggest blow.

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Rafael Devers also had a two-run double in the third, giving him 27 RBIs this month. Bogaerts’ single in the fourth off Chaz Roe drove in an eighth run charged to Beeks, a 26-year-old left-hander making his second career start.

The Red Sox, who are 6-5 since the All-Star break, pulled within one game of the Rays for third place in the AL wild card standings.

Tampa Bay has dropped six of seven and been outscored 41-17 over that stretch.

“It’s just one game, but it’s good to win the first one of the series,” said Benintendi, who was 3 for 5 and finished a triple shy of hitting for the cycle.

“We know what we need to do, we know where we stand,” the Red Sox outfielder added. “So we’ll take it one game at a time and see what happens.”

NO LONGER PERFECT — Beeks, who had won 10 consecutive decisions in relief since joining Tampa Bay in the trade that sent Eovaldi to Boston last July 27, allowed eight runs and seven hits over 2 1/3 innings in his first start since making his major league debut for the Red Sox against Detroit on June 7, 2018.

TRAINER’S ROOM —Red Sox: 1B Mitch Moreland, on the injured list since June 8 with a right quad strain, will be activated Tuesday. … INF Michael Chavis missed his second straight game since experiencing back spasms Saturday night. … RHP Steven Wright, who went on the injured list July 14 with a great right toe contusion, remains sore, according to manager Alex Cora.

Rays: Diaz left the game in the ninth after fouling a pitch off the inside of his left foot. He was sent for x-Rays after the game. … INF Matt Duffy, out all season with a strained left hamstring, could be reinstated from the 60-day injured list Tuesday. … Cash said All-Star INF Brandon Lowe, sidelined by a right shin bone bruise since July 3, is “still a ways away” from returning. … INF Daniel Robertson (right knee inflammation) started a rehab assignment with Class A Charlotte and went 0 for 2 with a walk.

UP NEXT — Three-game series continues tonight, with the Red Sox sending LHP Chris Sale (4-9, 4.05 ERA) to the mound against RHP Yonny Chirinos (8-5, 3.29), who’s 1-1 lifetime in five appearances against Boston, including three starts. Sale is 9-6 all-time vs. the Rays. His career 1.92 ERA at Tropicana Field is his lowest in any park where he’s made a minimum of five starts.

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