ST. PETERSBURG, Fla. — David Price had a flawless return from a nearly two-month layoff, but the Boston Red Sox missed a chance to pad their lead in the American League East, losing 3-2 Sunday to the Tampa Bay Rays.

The Red Sox managed just three hits against four Tampa Bay pitchers as the Rays avoided a series sweep. Jake Odorizzi (9-8) took a no-hitter into the sixth inning before giving up a game-tying two-run homer to Jackie Bradley Jr., but Jesus Sucre broke the tie in the bottom of the sixth with a home run off Eduardo Rodriguez (5-6).

Price, coming back from left elbow inflammation, pitched two perfect innings with two strikeouts in his first game since July 22, and his first relief appearance since 2010.

“I felt good. I put up two zeroes in a one-run game. It’s fun to get back out there,” said Price. “I felt good with the curveball, threw some really good cutters, a couple good changeups. It was good.”

The Red Sox remained three games ahead of the New York Yankees with 13 games remaining in the regular season. The Yankees lost 6-4 to Baltimore, which next hosts the Red Sox for a three-game series.

Errors by Rafael Devers at third base and Bradley in center field allowed Tampa Bay to score an unearned run in the first against Rodriguez. He allowed another run in the fifth on an infield single by Evan Longoria with the bases loaded, then gave up Sucre’s homer on his 110th pitch with two outs in the sixth.

Price was activated from the disabled list Thursday, and Red Sox Manager John Farrell had said he would go no more than two innings in his first appearance. The Red Sox will attempt to determine whether he can be stretched out enough to start in the postseason.

“That was even more than I personally anticipated,” said Farrell. “I’m amazed that someone who hasn’t pitched in a game in nearly seven weeks would come out with that kind of command and throw three or four pitches for strikes. He is a unique pitcher and that was really a strong two innings of work.”

Odorizzi retired 14 straight after a first-inning walk to Dustin Pedroia, but then walked Brock Holt to lead off the sixth. Bradley followed with a long drive to right field for his 17th homer.

According to Odorizzi, it wasn’t necessarily a bad pitch, just the wrong one.

“I was throwing what was working for me,” he said. “I had good life on my fastball. He was sitting dead-red. If I had thrown him a changeup, he probably would have swung and missed by a good bit. But I didn’t and he didn’t.”

Odorizzi pitched six innings, the longest of any Rays starter in their last 10 games.

Alex Colome pitched the ninth for his 45th save.

TRAINER’S ROOM

RED SOX: Right fielder Mookie Betts left the game in the fifth inning because of a right thumb contusion. His replacement, Rajai Davis, grounded into a double play to end the game. … Pedroia (left knee inflammation) returned to the line as the designated hitter after a day off following his 0-for-9 performance in Friday night’s 15-inning game. Pedroia will return to second base Monday night in Baltimore.

UP NEXT

RED SOX: Right-hander Doug Fister (5-8) will make his 13th start for Boston in the opener of a three-game series at Baltimore. Right-hander Dylan Bundy (13-9) will pitch for the Orioles.

RAYS: Former Tampa Bay Manager Joe Maddon will bring the Chicago Cubs to Tropicana Field for a two-game interleague series starting Tuesday night. Right-hander Chris Archer (9-10) will pitch for the Rays against left-hander Jon Lester (11-7).