"We needed to win that game," Derek Jeter said. "Wang deserves all the credit."
Meeting for the first time this season, the Indians and Yankees entered tied for the major-league lead with 359 runs apiece.
But Wang and Byrd silenced the offenses in an old-fashioned pitchers' duel, and New York's bullpen closed it out.
"That's one thing that has never changed in this game -- pitching can control the hitting," Yankees manager Joe Torre said.
After stranding five runners in his first two at-bats, Cano connected on a 1-1 pitch from Byrd (5-5) with one out in the sixth, sending a drive over the right-field fence.
"It was a hanging curveball," Byrd said. "He wasn't hitting anything soft off me, particularly. So I tried to locate it down and away. I just missed it. It's a shame that was the game."
The Indians had their best scoring chance in the top half, when Grady Sizemore led off with a double off the center-field fence and moved to third on a long flyout.
"It worked out perfect for them," Cleveland manager Eric Wedge said. "That kid has a real heavy sinker, too. It has some run on it as well as some down to it."
Aaron Boone reached on an infield single to start the eighth and advanced on a sacrifice, chasing Wang.
"Mo's got that glare about him right now," Torre said.
In his second major-league season, the 26-year-old Wang (7-2) pitched five-hit ball for 7 1/3 innings -- improving to 6-1 with a fill-in save in his past nine appearances.
"We needed him and he came through," Rivera said.
Wang walked one, struck out three and has allowed only one run in 14 1/3 innings over his last two starts -- against Boston and Cleveland.
"Most guys, if they make it to second, they say how good he is," Jeter said.
This performance was especially important for the Yankees, who had dropped four straight, all at home, to match their longest skid of the year.
"He goes out there and just goes about his business. I don't think he gets too concerned about what's going on," catcher Jorge Posada said. "You can call any pitch and you know where he's going to be."
Byrd yielded six hits and three walks in seven innings. He struck out six, tying a season high.
The Indians, blanked for the fourth time this year, have lost four of five and seven of 10.
"You hate to waste an effort like that," Boone said. "We just couldn't get much going and couldn't get that big hit. But Wang had a lot to do with that."
The Yankees put their leadoff batter on in each of the first five innings but Byrd pitched out of trouble.
Jeter was back at shortstop after three games as the designated hitter because of a bruised right thumb. He shook his hand in obvious pain immediately after a fifth-inning check swing that resulted in a 1-6-3 double play. But he made a strong, accurate relay throw on Martinez's double-play ball the following inning.
Bernie Williams went 2-for-3 in his 2,000th game for the Yankees, fifth on the franchise list behind Hall of Famers Mickey Mantle (2,401), Lou Gehrig (2,164), Yogi Berra (2,116) and Babe Ruth (2,084). "It's pretty remarkable. Especially now with the state of free agency," Jeter said. "That's why he's a fan favorite. It's been a pleasure playing with him for a lot of those games and watching him in grade school in the others." ... It was New York's third shutout this season and first 1-0 win since Sept. 17, 2005, at Toronto. ... Alex Rodriguez went 0-for-4 with three strikeouts and was booed lustily. ... Right fielder Gary Sheffield had surgery on his injured left wrist and is still expected back in September. ... Cano extended his hitting streak to 11 games. ... Cleveland has lost 13 of 15 at Yankee Stadium since the start of the 2002 season. ... Martinez pushed his hitting streak to 10 games. ... The Indians
have dropped nine of their last 12 road games.