Cano's pinch-hit homer snapped an eighth-inning tie, and Rodriguez hit No. 521 to match Hall of Famers Ted Williams and Willie McCovey on the career list during the New York Yankees' 8-7 victory over the Tampa Bay Rays on Monday night.
"It definitely humbles you," Rodriguez said. "I'm at a point in my career where you do some things and you start touching some of these names. It's hard to believe."
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.
"I think the team needed it a lot more than Robby," Rodriguez said. "Robby is going to be fine. Robby is a great hitter. He's going to hit well over .300, and probably make the All-Star Game."
It was Cano's second career pinch-hit shot.
"I hope to start from here," he said.
Mariano Rivera got four outs for his fourth save in four opportunities.
Kennedy said he was sore in the muscle area just below the hip bone, but expects to make his next start.
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.
Rodriguez has 36 games with four or more hits.
"A good character game," Girardi said.
Jeter returned to the lineup after missing the previous six games with a strained left quadriceps and went 2-for-5 with two RBIs.
"Everything feels fine," he said. "I didn't run as hard as I could. It's probably more mental than anything."
Kennedy allowed three runs and eight hits in six-plus innings.
Damon put the Yankees ahead with a leadoff homer in the first.
Rodriguez made it 2-0 later in the inning on his third homer of the season. The 448-foot drive to left stopped an 0-for-9 slide.
Ensberg extended the advantage to 3-0 with a second-inning 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.
"I'd like to have the A-Rod one back because up until tonight he hadn't gotten me before," Sonnanstine said. "But he's one of the best hitters in baseball."
Crawford got the Rays to 3-1 on a sacrifice fly in the third. Eric Hinske hit a run-scoring double one inning later.
"I love the fight," Rays manager Joe Maddon said. "We've got to stop making the mental mistakes that prevent us from winning games like tonight."
Rivera didn't get his fourth save last year until May 30. ... New York RHP Joba Chamberlain went on the bereavement list to be with his hospitalized father in Nebraska. ... Rays LHP Scott Kazmir (left elbow) pitched two innings in an extended spring training game. He could rejoin the team early next month. ... New York C Jorge Posada (right shoulder) is making progress in his throwing program, but there is no timetable for when he will return behind the plate. He is able to DH. ... The Yankees purchased the contract of C Chad Moeller from Triple-A Scranton/Wilkes-Barre. With backup C Jose Molina slowed by a left hamstring injury, Moeller was in the starting lineup.