"That was a huge win for us. A huge night by Robby," Rodriguez said after going 0 for 3 with a walk, a strikeout and a run scored in his ninth game since hitting his 599th homer on July 22. "We feel like we stole one tonight because they were pretty much in control all night."
Mark Teixeira and Nick Swisher also went deep for the defending world champions, who rallied from an early deficit against Matt Garza before Cano's drive into the right-field seats off All-Star closer Rafael Soriano (2-1) gave New York its 34th come-from-behind victory of the year.
"The way I'm swinging, it's probably going to take a while. Everybody get comfortable," Rodriguez said, smiling. "It's nice to be out there and helping the team somehow. Scored a run. People are asking me about home runs, I'm asking for hit by pitch, infield hit, bunt single, error. The home run will come, I hope. I'm going to be just fine. I think it's nice to contribute. I'm not just not swinging well right now."
Garza allowed four runs and five hits over seven innings in his first outing since pitching the first no-hitter in Tampa Bay history. He gave up a sacrifice fly to Curtis Granderson in the second and game-tying home runs to Teixeira and Swisher in the sixth and seventh innings.
Cano finished 3 for 4 with a pair of doubles. The homer was the 11th of his career at Tropicana Field, most of any road park where he's played.
"He's one of the best hitters in the league right now," Rays manager Joe Maddon said.
"The good things that he did tonight, that's certainly the look of an MVP," Rodriguez said. "That was a huge, huge hit against their closer on the road trying to protect first place. It doesn't get any better than that."
Teixeira's two-run shot erased a 3-1 Yankees deficit. Swisher's solo homer made it 4-all after Tampa Bay had regained the lead on Matt Joyce's two-out, sixth-inning homer off Javier Vazquez. Evan Longoria, Carl Crawford and Jason Bartlett also drove in runs for the Rays.
David Robertson (2-3) pitched a perfect eighth inning for the win. Mariano Rivera worked the ninth for his 22nd save in 24 opportunities, ending Tampa Bay's seven-game winning streak and increasing New York's lead over second-place Tampa Bay to two games in the AL East.
"This one falls on me," Garza said. "They spot me a two-run lead and I gave it away. They spot me another one and I gave it away. That's uncalled for. I had these guys beat, and I just gave it away. That's all there is to it."
The victory capped a busy day for the Yankees, who put together three deals before Saturday's trade deadline, acquiring slugger Lance Berkman from the Houston Astros and outfielder Austin Kearns and reliever Kerry Wood from the Cleveland Indians.
Berkman made his debut for his new team, batting second and going 0 for 4 with a strikeout as the designated hitter. Kearns was available off the bench, and Yankees manager Joe Girardi said there's a chance Wood could join the team in time for Sunday's season finale against the Rays.
"It's a ridiculous lineup," Garza said, explaining how the game got away. "Berkman comes in today and makes a tough lineup even tougher. ... I think they could field an All-Star team out there with the lineups they have."
Tampa Bay didn't make nearly as much noise before the 4 p.m. deadline, acquiring reliever Chad Qualls from the Arizona Diamondbacks but coming up short in other efforts to bolster the roster for the final two months of the regular season -- and possibly beyond.
Manager Joe Maddon said before the game that he wasn't concerned that the Yankees made some high-profile moves, while the Rays will go forward with essentially the same roster.
"From our perspective, we're good right now. We're playing well," Maddon said. "We did try to do some different things we thought could help us without interfering with what was going on. It did not want to happen, so your just turn the page and move on."
Garza, who walked one and struck out nine, limited the Yankees to a pair of doubles by Cano until Derek Jeter led off the sixth with a doubled over Joyce's head in right field. After Berkman fouled out, Teixeira brought a large contingent of New York fans among the sold-out crowd of 36,973 to their feet with his 21st homer to make it 3-all.
The right-hander settled to strike out Rodriguez and Cano to end the inning, but the Yankees weren't finished. After Joyce homered off Vazquez to put Tampa Bay up 4-3 in the bottom of the sixth, Swisher teed off on a 3-2 pitch from Garza leading off the seventh as New York pulled even again.
Swisher also homered in Friday night's 3-2 loss the Rays. His 12 homers against the Rays since the start of the 2009 season are the most by any player off Tampa Bay pitching.
Vazquez allowed four runs and eight hits over 6 1/3 innings. ... Teixeira was 1-for-15 lifetime against Garza before his home run. ... Tampa Bay 1B Carlos Pena left the game after the sixth inning because of soreness in his right foot. ... RHP Chan Ho Park, designated for assignment by the Yankees on Saturday, got a Rodriguez home uniform signed by the slugger before leaving the clubhouse. ... Qualls fills a need for the Rays with right-handed reliever Grant Balfour going on the 15-day disabled list with a ribcage strain. Balfour's injury was the result of what manager Joe Maddon described as horseplay between the reliever and pitching coach Jim Hickey.