Jeter, 37, said he felt no effects of the right calf strain that sent him to the disabled list three weeks ago. He remains six hits shy of becoming the 28th player -- and the first wearing a Yankees uniform -- to reach 3,000 hits.
"It's been kind of weird," Jeter said before Monday's game. "To be quite honest with you, now I just want to go out and play. I'm not going to think about it today. Hopefully, if I get a few hits one of these days, I'll think about it getting a little closer.
"At this point, I just want to go out and play a game, because I haven't played in a while."
In Jeter's first at-bat, he reached on an error by third baseman Lonnie Chisenhall, hitting a slow grounder on Josh Tomlin's second pitch of the game.
In the third inning, Jeter lifted a 2-0 fastball from Tomlin into the outfield, where Tribe center fielder Grady Sizemore collected it for the second out of the inning.
Jeter grounded out to Chisenhall for the second out of the sixth inning. He had one more chance, with one out in the eighth, facing reliever Vinnie Pestano and lining out hard to shortstop Asdrubal Cabrera.
"I actually felt good on a couple of them, especially the last one," Jeter said.
Jeter played in two Minor League rehabilitation games at Double-A Trenton over the weekend, and flew to Cleveland late on Sunday to re-join the Yankees.
With the Yankees' bullpen somewhat short, outfielder Chris Dickerson was optioned to Triple-A Scranton/Wilkes-Barre to make room for Jeter on the 25-man roster.
Yankees manager Joe Girardi said that putting Jeter back in the leadoff spot, which had been shared by Brett Gardner and Nick Swisher in Jeter's absence, was a simple decision.
"It was easy. It was like he never left," Girardi said. "You just put him right back in there. He played two days and he felt good, and that's a great sign for us."
Jeter said that he tried to keep up with the Yankees from afar, seeing mostly television highlights. Though he initially tried to fight his first disabled list assignment since 2003, Jeter acknowledged that the decision was a wise one.
"It feels good to be back," Jeter said. "I don't like to miss games, period, so to be out for three weeks -- it's tough to be away, because you want to be out there playing. In retrospect, it probably was the best thing to do."
Jeter said that he was impressed by the work that young Eduardo Nunez did filling in at shortstop. New York went 14-4 without Jeter, who strained his calf in a game against the Indians at Yankee Stadium on June 13.
"I wish they were 18-0, to be honest with you," Jeter said. "We want to win. When you have good streaks, you want them to last as long as possible. We did a great job, especially in Interleague Play. Hopefully it can continue."
Jeter was welcomed back to the Yankees' clubhouse with open arms, exchanging pleasantries with teammates who missed his presence.
"We all know what kind of person Jeter is, what kind of player he is," second baseman Robinson Cano said. "It's always good to be around him."
After two more games in Cleveland, the Yankees open a four-game homestand at Yankee Stadium against the Rays on Thursday, leading into the All-Star break.
The Bombers return from the break with an eight-game road trip to Toronto and Tampa Bay, but Girardi said that his priority was to get Jeter past the next six hits as quickly as possible, regardless of whether the milestone comes in the Bronx.
"I want him to get to 3,000 as soon as he can," Girardi said before Monday's game. "I'm going to manage him more from a physical standpoint than the 3,000 hits."