The infield single knocked a hobbling Kennedy out of the game, and Tampa Bay hit three quick homers off New York's bullpen before the inning was over to tie the score at 7.
Carl Crawford hit a two-run homer off left-hander Billy Traber. B.J. Upton added a two-run drive off winner Brian Bruney, then rookie Evan Longoria connected against Bruney (1-0) for his first major league home run.
But Cano, who entered hitting .170 and was rested by manager Joe Girardi, came off the bench to put the Yankees back in front with a long homer to right off Al Reyes (1-2).
Rodriguez connected in the first inning against Andy Sonnanstine and finished with four hits. A-Rod tied Williams and McCovey for 15th place on the career home run list.
The homer also was A-Rod's 176th with the Yankees, moving him past Bobby Murcer for 19th on the franchise list. The slugger, who went 4-for-5, also scored his 500th run with New York on the homer.
Johnny Damon and Morgan Ensberg also homered for the Yankees, who scored more than six runs for the first time this season.
Jeter returned to the lineup after missing the previous six games with a strained left quadriceps and went 2-for-5 with two RBIs.
Mariano Rivera got four outs for his fourth save in four opportunities.
Kennedy allowed three runs and eight hits in six-plus innings.
Damon put the Yankees ahead with his 23rd leadoff homer. It was the first time he has done it since last May 30.
Rodriguez made it 2-0 later in the first on his third homer of the season. The 448-foot drive to left off stopped an 0-for-9 slide.
Ensberg extended the advantage to 3-0 with a second-inning solo homer.
Damon drove in two more runs with a double and Jeter hit a two-run single as the Yankees took a 7-1 lead in the fourth.
Sonnanstine gave up seven runs and nine hits in 3 1-3 innings.
Crawford got the Rays to 3-1 on a sacrifice fly in the third. Eric Hinske hit a run-scoring double one inning later.
