ST. PETERSBURG, Fla. -- Evan Longoria had another memorable at-bat during his outstanding rookie season.
Longoria's two-run drive in Tampa Bay's four-run seventh was his 22nd of the season, setting a team record for a rookie. Longoria hit two long drives that landed in foul territory then took a pitch before connecting against Rafael Betancourt.
"Longo's at-bat was spectacular," Rays manager Joe Maddon said. "He thought the first foul ball he hit was the hardest ball the whole at-bat."
Longoria's 428-foot drive made it 6-3, and Floyd and Navarro added back-to-back shots later in the inning.
Longoria hit a grand slam off Toronto ace Roy Halladay on July 20 during a 10-pitch at-bat. He fouled two balls off his left ankle before the homer.
Edwin Jackson (8-7) won his third consecutive start, giving up three runs and seven hits in 5 2/3 innings. Four Rays relievers allowed one run over the final 3 1/3 innings
"You've got to be thankful for them," Floyd said of the bullpen. "If we're going to win, it's going to take them to keep doing what they've been doing."
Left fielder Carl Crawford (sore left hamstring) and shortstop Jason Bartlett (right index finger) were out of the Rays lineup for the second consecutive game.
Tampa Bay stayed three games ahead of Boston and moved 6 ½ games ahead of third-place New York.
Jhonny Peralta hit a two-run homer in the third to put Cleveland ahead 3-1. He has six homers and 26 RBI over his last 25 games.
Tampa Bay responded with three runs in the fourth. Navarro stopped an 0-for-14 slide with a two-out, two-run single, and scored on Gabe Gross' triple to give the Rays a 4-3 lead.
"I really believe we showed a lot of heart," Maddon said. "We wanted to win that game, and somehow we did. These guys (Cleveland) have pressed us hard."
Grady Sizemore had an RBI single in the eighth for Cleveland, which had won the first five games in the season series against Tampa Bay. The Indians left 13 runners on base, and went 2-for-16 with runners in scoring position.
"It was a frustrating ballgame to say the least," manager Eric Wedge said.
Indians right-hander Fausto Carmona (5-4) lasted just four innings in his third start since returning from a left hip strain. He allowed four runs and three hits, walked five and struck out four.
Carmona has given up 17 runs over 12 2/3 innings in his last three outings.
"It's been a little difficult to get in a good groove, especially today," Carmona said through a translator. "I was trying to get back into the strike zone, but I was unable."
Shin-Soo Choo put the Indians ahead 1-0 with an RBI single in the first. The Rays tied it at 1 in the bottom half on Carlos Pena's sacrifice fly.
Cleveland loaded the bases with two outs in the sixth, but failed to score. Rays outfielder B.J. Upton caught pinch-hitter Ben Francisco's drive near the center-field fence to end the inning.
Jonny Gomes held the Rays' previous record for homers by a rookie, hitting 21 in 2005. ... The bat used by Indians C Kelly Shoppach during his major league record-tying five extra-base hit game on July 30 against Detroit has been sent to the Hall of Fame. ... Tampa Bay recalled SS Ben Zobrist from Triple-A Durham and optioned Gomes to its top farm club. ... Indians 3B Andy Marte stopped an 0-for-20 skid with an eighth-inning double.