ST. PETERSBURG, Florida — Matt Joyce needed just one swing to overcome a tough day.
"A nice finish," said Joyce, who was hitless with two strikeouts in four earlier at-bats. "I was excited about the opportunity."
Ryan Hanigan opened the 10th with a double off Burke Badenhop (0-3), which withstood a replay review. Kevin Kiermaier was intentionally walked before Ben Zobrist had a sacrifice bunt. After Wil Myers was given an intentional walk, pinch-runner Sean Rodriquez, who ran for Hanigan, scored on Joyce's hit to left.
"It worked out pretty well," Rays manager Joe Maddon said.
Grant Balfour (2-6) worked a scoreless inning for the win. He did give up a one-out single in the 10th to Christian Vazquez, but then picked off pinch-runner Jemile Weeks at first base.
After Mike Napoli hit a solo homer in the fourth inning, Yoenis Cespedes got the Red Sox even at 3-3 with an RBI single off Steve Geltz in the eighth.
Myers had an RBI double and Evan Longoria drove in two with a single off Rubby De La Rosa as the Rays took a 3-1 lead in the third.
Myers, who entered hitting .143 (6 for 42 with 16 strikeouts) since returning from a broken right wrist, finished with three hits in four at-bats. Longoria has 34 RBIs in 41 games since the All-Star break.
De La Rosa allowed three runs and six hits over 5 1-3 innings.
Drew Smyly, who on Wednesday at Baltimore became just the second Tampa Bay pitcher to have consecutive starts of seven or more innings and two hits or fewer, gave up two runs and three hits in 5 2-3 innings.
Mookie Betts put the Red Sox up 1-0 with a run-scoring double in the third.
Boston designated hitter David Ortiz, who recently fouled a ball of his foot, got the day off. Second baseman Dustin Pedroia sat out his second straight game due to concussion-like symptoms.
"I feel normal but I've got to take all these tests and stuff, which is kind of tough," Pedroia said. "I haven't passed many tests in my schooling life."
The announced crowd at Tropicana Field was just 10,543.
Red Sox: Manager John Farrell said Pedroia could miss a three-game series with the New York Yankees that starts Tuesday.
Rays: CF Desmond Jennings (sore left knee) was out of the lineup for the fourth straight game but was available off the bench. ... OF David DeJesus (broken left hand) was activated from the 15-day disabled list after missing 64 games.
Cuban CF Rusney Castillo, signed to a $72.5 million, seven-year contract last month, went hitless in three at-bats with a bases-loaded walk in his second game with the Gulf Coast League Red Sox. Expected to join the Red Sox later this month, Castillo will now join Double-A Portland.
Rays: RHP Brandon Gomes was recalled from Triple-A Durham, while Geltz had his contract purchased from the International League club. ... C Curt Casali was recalled from Single-A Charlotte. ... C Ali Solis was outrighted to Durham.
Red Sox: RHP Joe Kelly (0-1) is scheduled to face Yankees RHP Shane Greene (4-1) Tuesday night.
Rays: RHP Jeremy Hellickson (1-2) and knuckleballer R.A. Dickey (10-12) are the scheduled starters in the start of a three-game series Tuesday night.