The Phillies, who've lost 10 of 12, scored four runs in the first, but rookie left-hander Antonio Bastardo (2-3) couldn't hold the lead.
Andy Sonnanstine (6-7) allowed four runs in 5 1-3 innings, but got the win.
The Rays scored six times in the first two innings, then broke the game open with three runs in the sixth off Chad Durbin.
Aybar, starting because Longoria was resting a sore left hamstring, had a solo homer in the second and a two-run single in the sixth.
Zobrist's 16th homer finished Tampa Bay's three-run first. Bartlett had two singles, one of them driving in a run in the sixth, to prolong his hitting streak. Quinton McCracken had an 18-game streak for the Rays in 1998.
Sonnanstine settled after yielding a two-run double to Ryan Howard, an RBI double to Matt Stairs and an RBI single to Pedro Feliz in the first. The right-hander allowed six hits, walked one and struck out seven.
With Scott Kazmir ready to come off the 15-day disabled list, Sonnanstine - a 13-game winner a year ago who has been inconsistent this season - may well have been pitching to retain his spot in the rotation.
Kazmir likely will make his first start in more than a month this weekend against Florida, and manager Joe Maddon faces a decision on whether Sonnanstine, rookie David Price or Jeff Niemann will be moved to the bullpen or minor leagues.
The Rays answered Philadelphia's quick start with three runs in the first and three more in the second against Bastardo, who allowed six runs and seven hits before leaving with a shoulder sprain with one out in the fourth.
After the shaky beginning, Sonnanstine allowed one hit - Greg Dobbs' one-out single in the fifth - over the next four innings. The only other Phillies baserunner during that stretch reached on a walk in the third.
The Phillies, who played without slumping shortstop Jimmy Rollins, wasted an opportunity to cut into a two-run deficit in the sixth, when Feliz was doubled off first base on one-out fly ball to center that should have scored Matt Stairs from third.
Feliz scrambled to get back to first and Stairs took off for home, but B.J. Upton's throw from center easily beat both runners for the third out.
Rollins, hitless in his last 19 at-bats, will be out of the starting lineup at least two games.
Phillies manager Charlie Manuel said he wants Rollins, who's hitting .211, to "sit and watch and relax."
Notes: The game was delayed 1 minute, 36 seconds in the seventh inning while the umpires used instant replay to determine if there was fan interference on Pat Burrell's ground-rule double that bounced into the left-center field stands. There wasn't. ... Longoria expects to return to Tampa Bay's lineup Friday night against Florida. ... The Phillies reinstated closer Brad Lidge (sprained right knee) from the 15-day disabled list.
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