Mussina (6-3) allowed one run and five hits over 6 1-3 innings to win his fifth consecutive decision. He improved to 18-7 in 31 starts against Tampa Bay, which held on to its slender lead in the AL East.
Cano, who tied a career high with four hits, had a RBI single in the fourth. Bobby Abreu drove in New York's other run off James Shields (4-3) with a two-out double in the fifth, and shortstop Derek Jeter started a nifty double play to end a Tampa Bay threat.
Joba Chamberlain struck out the side in the eighth - and didn't pump his fist. Mariano Rivera bounced back from allowing the winning run in an 11-inning loss the previous night with a perfect ninth for his 11th save in 11 opportunities.
Tampa Bay's loss snapped a franchise-best 11-game home winning streak. But the first-place Rays retained a half-game lead over Boston in the division, thanks to Baltimore beating the Red Sox 6-3.
The Yankees held a 35-minute team meeting before the game, however Girardi said it had nothing to do with Steinbrenner's comments earlier in the day - the co-chairman said the team needs to play harder and smarter.
Girardi declined to offer details except to say the meeting came from his "heart."
"The effort of the club has been good," he said. "When you don't score runs, you don't look good. We bring energy every day, but the bottom line is it has to translate into wins."
The Yankees entered Wednesday night losers of five of seven and had only scored two runs in dropping the first two games of the series to the surprising Rays.
Shields is one of Tampa Bay's top young pitchers and big part of the team's climb to the top of the standings. He was coming off a one-hit shutout of the Los Angeles Angels, but has struggled throughout his against the Yankees.
Cano's RBI single snapped a scoreless tie and Abreu's pop fly down the left-field line dropped for a run-scoring double that made it 2-0. That was all the support Mussina would need to get his 109th win as a Yankee.
Carlos Pena had two of Tampa Bay's five hits off the Yankees starter, who walked one and struck out four before being replaced by Ross Ohlendorf with a runner of first and one out in the seventh.
The first two batters the reliever faced, Cliff Floyd and Dioner Navarro, singled to break up the shutout. Ohlendorf avoided further damage when Gabe Gross' hard liner that appeared to be head for left center was snagged by Jeter, and Floyd was doubled off second base to end the inning.
Shields fell to 0-6 in seven career starts against the Yankees, who also beat him 2-0 in New York on April 6.
