ST. PETERSBURG, Fla. -- Boston Red Sox center fielder Mookie Betts made a base-running mistake in the seventh inning that erased a chance to score the go-ahead run.

He made up for it in the 10th inning.

Betts hit a leadoff double in the 10th, extending his hitting streak to 13 games, and second baseman Brock Holt's RBI single brought him in as the winning run in a 4-3 victory over the Tampa Bay Rays on Friday night at Tropicana Field.

"Mookie, we've seen it a number of times where something hasn't worked out for him, and he comes right back to find a way to contribute, none bigger than the leadoff double," Red Sox manager John Farrell said. "We know what's happened has happened. We can't go back."

Boston (33-42) improved to 3-2 in extra-inning games this season, with closer Koji Uehara getting two strikeouts in a 1-2-3 10th for his 15th save.

Tampa Bay (41-34) remains in first place in the American League East despite losing four of the last five games, including two straight in extra innings.

"It's definitely frustrating," said Rays outfielder Steven Souza, who went 0-for-4 with two strikeouts, including one to end the eighth with a runner on. "We had several situations, mine included, to get the job done and we just didn't get it done, plain and simple. In order to win ballgames like that, we've got to come up with a clutch hit in those big opportunities."

Down 3-1 in the sixth, the Rays rallied to tie the game, with designated hitter Joey Butler walking and third baseman Evan Longoria hitting a double off the wall in right field to lead off the inning. Left fielder David DeJesus hit a sacrifice fly to score Butler, with Longoria tagging up and advancing to third. Longoria then scored to tie the game on a wild pitch by Red Sox starter Rick Porcello.

The Red Sox had the go-ahead run in scoring position -- briefly -- with one out in the seventh, as Betts stole second base with the throw sailing high into center field. But Betts hesitated as he headed for third, and a quick throw from center fielder Kevin Kiermaier got him tagged out at third base.

The Rays also had Longoria at second with one out in the eighth, but he was tagged out at third after a quick throw from shortstop Xander Bogaerts on a ground ball from second baseman Logan Forsythe.

Tampa Bay got a leadoff double from shortstop Asdrubal Cabrera in the ninth, and got him to third with two outs, but Butler lined out to right field to end the rally and send the game to extra innings.

The Red Sox led 3-1 after five innings, led by strong pitching from Porcello, who had five strikeouts at that point and benefited from two double plays.

"He kept us in the ballgame. Quality start for him," Farrell said of Porcello, who gave up nine hits but left after six innings with the game tied at 3-3. "I thought he threw the ball fairly consistently until that sixth inning."

Boston had only four hits in the first six innings, but made the most of them to build an early lead. Left fielder Alejandro De Aza got the scoring started with an RBI double in the second inning, driving in first baseman Mike Napoli, who had walked. De Aza advanced to third on a groundout and scored on a sacrifice fly by right fielder Jackie Bradley for a 2-0 lead.

The Rays answered with a run in the second, as first baseman Marc Krauss, making his Rays debut after being acquired in a trade with the Angels, ripped an RBI double down the right-field line in his first at-bat with Tampa Bay. Krauss, who also made an impressive catch of a foul ball right in front of the Rays dugout in the first, was stranded when catcher Curt Casali grounded out to end the inning.

Napoli scored again in the fourth inning, again walking and advancing to third on a single by catcher Blake Swihart. He scored when Swihart was thrown out attempting to steal second, extending Boston's lead to 3-1. Rays starter Alex Colome held Boston to four hits through five innings, but hurt himself with five walks.

"I felt good today. Not the best start, but I fought the hitters," Colome said. "I tried to be too perfect sometimes. In the first few innings, I threw too many pitches. ... Maybe if I don't walk anybody or walk one or two guys, we have a chance to win."

NOTES: The Rays, who struggled to find a short-term answer at first base with James Loney on the disabled list, acquired Marc Krauss from the Angels for minor league RHP Kyle Winkler. Krauss, 27, made his Rays debut Friday night, playing first and batting eighth. To make room for Krauss, the Rays optioned INF Nick Franklin to Triple-A Durham. ... Red Sox OF Shane Victorino (calf) played his second rehab game Thursday for Triple-A Pawtucket, going 2-for-3 with a run and a double. He was scheduled to have Friday off. ... Red Sox C Ryan Hanigan (right hand fracture) continues his rehab at Pawtucket, where he is 2-for-10 in three games with two walks and two runs scored.