Lee logged his sixth victory in the effort, outdueling right-hander Chien-Ming Wang, who turned in a quality seven-inning start on an evening when the Yankees could muster no backing.
Outfielder Johnny Damon said that Lee -- who struck out seven and has walked none in his last 28 innings -- was a tough customer from the very beginning.
"I thought in the first inning he was pretty nasty," Damon said. "His fastball had some life and some movement. They had a lead, and he just kept attacking the strike zone. I'd say his record is definitely well deserved."
But the Yankees had their chances, especially beginning in the fifth inning, after Lee had cruised on one hit through the first four frames. In the fifth, Melky Cabrera and Robinson Cano reached on one-out singles, but Lee struck out Morgan Ensberg swinging and got Jose Molina to fly out, ending the threat.
The Yankees' troubles didn't end there. New York also left two in scoring position in the sixth, when Hideki Matsui whiffed on a tough 1-2 curveball, stranding Bobby Abreu and Shelley Duncan. New York left seven in all.
"I had thrown [Matsui] a couple of fastballs away," Lee said. "He wasn't really getting around on it. [The curveball] is not a pitch you want to throw for a strike to hit. But if I keep it down, it's an effective pitch."
Frustration showed in the seventh, when Molina spiked his bat to the grass after Lee struck him out to end the inning, leaving a runner on and completing the lefty's night after 103 pitches.
It has been a remarkable turn for Lee, who began last season on the disabled list, was optioned to Triple-A Buffalo and did not appear on Cleveland's playoff roster. Damon believes that the Yankees missed their chances.
"His fastball was a little flatter, and we just weren't able to capitalize," he said. "If we did hit a ball hard, it was on the ground, and the grass slowed it up. He did exactly what he needed to tonight."
Manager Joe Girardi credited Lee's ability to throw first-pitch strikes and get ahead in the count, which kept New York's hitters on the defensive.
"You want to make him work, but it's tough when you're 0-2 all the time," Girardi said. "You want to be patient and try to get a good pitch to hit, but he's living on the corners and he's living ahead, and he's able to pitch in and out. He's able to move the ball around, and it makes it difficult to have long at-bats against him."
Lee combined with Rafael Perez and Rafael Betancourt for the shutout, the third suffered by the Yankees this season and their second against a left-handed starter, having been blanked by the Orioles' Brian Burres on April 19.
The Indians got to Wang early, scoring once in the first inning and tacking on runs in the fourth and fifth.
Victor Martinez's sacrifice fly brought home Grady Sizemore with Cleveland's first run, and Casey Blake and David Dellucci added run-scoring hits to stake Lee to a three-run lead.
"I tried last time to use the sinker in and outside, but today the control was not too good. I was behind in the count," Wang said.
Wang opened the year with six wins and seven team victories through his first seven starts, and he had won his previous 11 starts immediately following a Yankees loss. On Wednesday he appeared to give up more well-struck fly balls and liners than usual.
Wang took his first loss of the season, falling to 17-2 in his career against the AL Central. Both regular-season losses have come against the Indians, the other coming on July 3, 2006, at Cleveland -- to say nothing of his two defeats in last year's AL Division Series.
Still, Wang gave the Yankees a good enough start to win, a familiar theme in the first two games of this series. On Tuesday, Andy Pettitte threw 6 1/3 innings of strong two-run ball before Joba Chamberlain served up a three-run homer in the eighth.
Girardi finds the turn of events difficult to swallow.
"It's frustrating, because that's what you ask your pitchers to do," he said. "You ask them to give us an opportunity to win games. Both nights they've done that."