David Price (10-10) held New York to six hits and one run over eight innings opposite Sabathia (16-7), who lasted eight frames as well despite a rare penchant for allowing the long ball.
Sabathia was looking to rebound from a poor showing against Boston last Saturday when he surrendered seven runs over six innings.
But the Rays continued the left-hander's mini-slump in the most unlikely of ways. Sabathia entered the game with a 0.39 HR/9.0IP ratio, the third lowest in the majors this season. He was also working on a 56 1/3-inning homerless streak at Yankee Stadium, a record for the nearly three-year-old park.
Kotchman broke the stretch leading off the third inning by hooking a home run just inside the right-field foul pole. Shoppach followed with a blast to left- center, and three batters later, Damon turned on a middle-in fastball -- roughly the same pitch pounded by Kotchman -- and made it 3-0 in the blink of an eye.
Johnson and Longoria tacked on leadoff homers in the fifth and eighth innings, respectively.
"You're going to give up some runs, even the greatest starters get hit around sometimes. He's just going through a little streak right now," Yankees manager Joe Girardi said of his starter.
Overshadowed by Sabathia's misery, Price was effective in his outing, throwing 73 of his 114 for strikes.
"[Price] was able to throw all his breaking stuff really well and keep them off balance," Shoppach said of his battery mate.
Joel Peralta struck out the side in the ninth to finish off the gem.
The last Yankees pitcher to yield five home runs in a game was in David Wells on July 4, 2003...Sabathia had allowed five home runs over his previous 16 games combined.