"We're clicking pretty good, offensively," said Giambi, who has four homers in his last three games. "We're playing great defense, and the pitching is really coming around."
The win was the fifth in a row for the Yankees, who climbed within 3 1/2 games of the first-place Red Sox and two games of the Wild Card-leading Twins.
"I think we realize that we're a good ballclub," Mussina said. "Nobody has run away from us in this division, so even if we're not five games up at the break, we're not buried. As inconsistently as we've played, we still have a chance to be there at the end of the summer."
Cabrera went 1-for-4 and recorded four putouts.
"He took charge in center, which is the main reason he's out there," said manager Joe Torre. "Anything he gives us, offensively, is a bonus."
Cleveland had won nine of 13 entering the four-game series, but the Yankees struck quickly and never looked back.
A-Rod got things started for the Yankees, drilling a two-run homer off starter Kevin Millwood in the first inning. It was A-Rod's 22nd homer, tying him with Boston's Manny Ramirez and Texas' Mark Teixeira for tops in the American League.
"I didn't get all of it, but I got enough of it," Rodriguez said. "It's a big lift for us to get Moose a cushion."
The Tribe got one run back in the second on Jhonny Peralta's 10th homer, a solo shot off Mussina, but Giambi boosted the lead back to two right away, belting a solo shot to lead off the bottom of the second.
"I'm hitting the ball good," said Giambi, whose recent surge has re-energized the lineup. "I've worked hard to get to this point, and I finally feel good, physically."
"It's all confidence right now," said Torre. "His at-bats are all quality. He's locked in pretty good right now."
Cleveland plated a second run in the fifth, trimming the lead to one on an RBI fielder's choice by Grady Sizemore. But the Yankees broke out with three runs in the sixth, two on RBI singles by Hideki Matsui and Giambi, with a third run scoring on a Millwood wild pitch. Giambi finished the night 2-for-3 with two RBIs.
"He's in a good groove," Torre said. "He's feeling pretty good about himself."
Jeter added a solo shot against Fernando Cabrera in the seventh, his 11th of the season. The Yankees have now hit 11 home runs in the past three games.
Mussina (9-5) left the game after seven innings, charged with two runs on six hits, striking out five.
"I was able to throw some breaking balls for strikes, got some ground balls for outs and had a couple of quick innings," Mussina said. "It was a nice, well-played game. We didn't make any mistakes, which is the way we've been playing lately."