ST. PETERSBURG, Fla. -- With the Tampa Bay Rays clinging on to fading hopes to sneak into the postseason, Evan Longoria and Jesus Sucre made sure they would survive for another day.

Longoria had two RBIs and Sucre hit a solo home run to lift the Rays to a 3-2 win against the Boston Red Sox at Tropicana Field on Sunday.

Tampa Bay (73-77) salvaged the final game of the three-game set against the Red Sox to keep its fading hopes at the second American League wild-card spot alive.

"We needed a bounce back after two tough losses," Rays manager Kevin Cash said. "(Jake) Odorizzi threw the ball really, really well to say the least. Bullpen came in and did their thing and then Jesue Sucre -- they tie it up and he answers right back."

Boston (85-64) had its three-game win streak snapped.

Rays starter Jake Odorizzi pitched five innings of no-hit ball before running into trouble in the sixth inning. Odorizzi gave up a lead-off walk to Brock Holt and then served up a fastball that center fielder Jackie Bradley sent over the right-field wall for a home run that tied the game 2-2.

"I was just throwing what was working for me," Odorizzi said. "I had good life on my fastball and he was sitting dead-red on it. 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. I was just going with my strength right there and what was working well for me that day and he hit it. Good for him."

Sucre put the Rays ahead again in the bottom of the sixth when he hit a solo shot off Red Sox starter Eduardo Rodriguez to make the score 3-2.

"Just (trying to) go away for a strike, on the outside corner for a strike," Rodriguez said. "And I just missed it right in the middle of the plate."

Rodriguez and Sucre, friends from their native Venezuela, joked about the pitch before it happened.

"When I got my first hit he was looking at me when I was inside and he was like 'I'm not going to throw you a fastball,' " Sucre said. "So he did, he threw me one fastball right there, I got a pretty good swing on it."

Alex Colome closed out the game for his 45th save, which leads the major leagues.

Longoria had an RBI single in the first inning that scored Kevin Kiermaier and added an RBI single with the bases loaded in the fifth that scored Sucre.

Odorizzi (9-8) gave up the one hit and two runs over six innings and struck out six.

Rodriguez (5-6) gave up three runs, two earned, and seven hits in 5 2/3 innings. He struck out seven.

"I thought he pitched and used all his stuff very well today," Red Sox manager John Farrell said. "We didn't really help him too much defensively in the first inning but he was able to get a number of key strikeouts with men in scoring position. All along I thought he used all three pitches really well."

Red Sox pitcher David Price, in his first bullpen appearance since coming off the disabled list, threw two scoreless innings in relief.

"I felt good," Price said. "I put up two zeroes in a one-run game. It's fun to get back out there."

NOTES: Red Sox manager John Farrell had no additional updates on INF Eduardo Nunez (knee) or 1B/DH Hanley Ramirez (shoulder, biceps) and said INF Dustin Pedroia (knee) would play 2B on Monday. ... Rays 1B Logan Morrison (lower back soreness) was not in the starting lineup for the third consecutive day and is hitless in his last 19 at-bats. ... Red Sox OF Mookie Betts left Sunday's game in the fifth inning with a right thumb contusion. He is day-to-day. Farrell said X-rays were negative.