They did so owing a major "thank you" note to the long ball. Cano's deep drive gave the Yankees the lead, but Mark Teixeira and Nick Swisher earlier connected for roundtrippers off starter Matt Garza that erased Rays leads.
"We feel like we stole one tonight, because they were pretty much in control all night," said Alex Rodriguez, who went hitless in three at-bats with a walk and a run scored, and continues his long wait for career homer No. 600.
But the fact that Cano answered the call in a pressure spot should come as no surprise to the Yankees, who have been watching their All-Star's breakout campaign all season long.
"I went up there and just tried to have a good swing to get on base for my teammates. I hit it out," Cano said.
Cano is already widely regarded as one of the best -- if not the best -- second basemen in the game, and A-Rod believes Cano may be charging toward even bigger things.
"When you do things like he did tonight, that's certainly the look and the taste and the feel of an MVP," he said. "That was a huge, huge hit against their closer, on the road, trying to protect first place. It doesn't get any bigger than that."
Teixeira had tied the score in the sixth inning with a two-run homer off Garza, his 21st, and after the Rays regained the lead on a Matt Joyce blast that left Javier Vazquez slapping his glove, Swisher answered in the seventh, taking Garza deep for his 20th home run, a solo blast.
"It's a ridiculous lineup, you know," Garza said. "I don't know what to say. I don't know how many All-Stars are on that team. I think they could field an All-Star team with the lineups they have."
Garza's final line was sullied by the homers, as he was charged with four runs on five hits in seven innings, but his nine strikeouts made him no picnic for the Bombers, who can post a series victory with a win on Sunday.
"Garza was on his game today," Swisher said. "I felt like every strike was right on the corner. He mixed his pitches, he had a good breaking ball tonight, and it was just a big game for us. ... To be able to come back today and battle, fight and get those late home runs was huge."
The Rays took a lead in the first inning against Vazquez when John Jaso doubled, moved up on a bunt single and scored on Evan Longoria's sacrifice fly.
Rodriguez walked and scored on Curtis Granderson's sac fly in the second inning to tie the score, buoying hopes that the Yankees' offense would be offering Vazquez some elusive run support on a night when he needed it.
"They were great all night," Vazquez said. "I gave up a run here and there, and they just kept coming back."
Tampa Bay added a run in the third inning when Jaso stroked a one-out triple to left-center that eluded Brett Gardner, and scored on Carl Crawford's RBI single. The Rays extended the advantage in the fifth when B.J. Upton doubled and scored on a Jason Bartlett sacrifice fly.
Joyce hit his second homer in as many nights in the sixth inning, this one off Vazquez, clipping the "C" ring catwalk above right field and allowing the Rays to enjoy a brief one-run lead before it again vanished.
"It's one of those pitches where he guessed right, and he got it. He didn't miss it," Vazquez said.
The Yankees also enjoyed spotless relief from their bullpen. Boone Logan got two outs to bail Vazquez out of the seventh inning, and Dave Robertson hurled a scoreless eighth, setting up Mariano Rivera to pitch the ninth inning for his 22nd save after Cano's homer had provided the lead.
"The top of the order was extremely tough on us tonight," manager Joe Girardi said. "It's just an outstanding relief appearance for our guys."
It also made for a nice welcome for new acquisitions Lance Berkman and Austin Kearns, who were obtained in advance of Saturday's non-waiver Trade Deadline. Berkman went 0-for-4 in his debut, but he quickly came to enjoy the perks of jumping into the AL East pennant race.
"It was definitely sort of a playoff-type atmosphere," said Berkman, who was acquired from the Astros for two Minor Leaguers. "Maybe not quite the intensity, but pretty dang close.
"Coming from where I've been, it was very intense. I enjoyed it. I thought it was a good atmosphere. We've got to play these guys a bunch more -- I was looking at the schedule. This won't be the last one of these types of contests."