Gomes, who spent six seasons with Tampa Bay from 2003-08, hit his fifth home run of the season off reliever Joel Peralta (0-1) to stop the Rays' six-game winning streak.
Carlos Pena, Ben Zobrist and Elliot Johnson all homered as Tampa Bay rallied to bail out Jeremy Hellickson after an ineffective start. But the Rays fell to 13-2 at home and failed in their bid to become the first major league team to reach 20 wins this season.
The A's worked long at-bats to run up Hellickson's pitch count and chase last year's AL Rookie of the Year after 3 2-3 innings.
Hellickson threw 52 pitches through two innings and finished with 102 in the shortest outing of his young career. He gave up three runs, two earned, on five hits and three walks.
Josh Reddick also homered for the A's. Brian Fuentes (2-0) worked two scoreless innings and Grant Balfour, another former Ray, got three outs for his seventh save in nine chances.
Tampa Bay had a chance to win in the 11th when Sean Rodriguez reached third with one out after a leadoff double that dropped between three players in shallow right field. Johnson, however, struck out when he fouled off a suicide squeeze attempt with two strikes and Desmond Jennings flied out.
Johnson homered in the third, Zobrist in the fourth and Pena in the fifth to tie the game. All three came from left-handed hitters - manager Joe Maddon intentionally put six left-handed bats in Tampa Bay's lineup.
Oakland starter Bartolo Colon had held left-handed batters to a .198 average coming in, but he ended up throwing 83 pitches over five innings and giving up eight hits.
Reddick hit his fifth homer in the first and Cliff Pennington scored in the third after reaching on an error by second baseman Ben Zobrist. Kila Ka'aihue drove in Pennington with a single, and Reddick added an RBI single in the fourth.
Rays relievers J.P. Howell, Jake McGee, Burke Badenhop and Fernando Rodney picked up the slack for Hellickson. Brandon Gomes worked himself out of a bases-loaded jam in the 10th.
NOTES: It was Maddon's 1,000th game as Tampa Bay's manager. He is 514-486 in seven seasons. The club had just 518 wins prior to his arrival. ... Maddon became the fourth manager with at least 1,000 games with his current team. He joined Mike Scioscia (1,972) of the Angels, Minnesota's Ron Gardenhire (1,647) and Philadelphia's Charlie Manuel (1,162). Detroit's Jim Leyland will join the group Sunday. ... Balfour has 17 career saves, tying him with Graeme Lloyd for most by an Australian-born pitcher. ... Will Rhymes made his third start at third base, the most of any Rays player since Evan Longoria was placed on the disabled list Tuesday. ... Pena snapped a 0-for-12 slump with an infield single in the first. ... The loss snapped a streak of six consecutive wins on Cinco De Mayo for the Rays. ... The announced attendance was 23,890. ... Oakland leadoff batter Jemile Weeks went 0 for 6.