Franklin Gutierrez's tiebreaking single in the ninth inning Sunday night sent the Indians past Texas 4-3 for their season-high seventh straight win and a three-game sweep of the fading Rangers.
Reyes didn't get the win because Rafael Betancourt walked in the tying run in the eighth, but that didn't change Cleveland's reaction to Reyes' fourth start since coming over in a trade with St. Louis in July.
"I thought he threw the ball very well," Indians manager Eric Wedge said. "Over the last couple of innings, he picked up a little steam. I think he was sniffing it (a win)."
The Indians were up 3-1 through seven after Reyes threw a season-high 107 pitches, allowing one run and four hits with four strikeouts and four walks.
There were high expectations for Reyes in St. Louis. He won a World Series game for the Cardinals in 2006, then went 2-14 the following year. The Cardinals sent him to the minors twice this season, and he was on the disabled list in June and July with a right elbow strain before being traded to Cleveland.
"It seems like I'm having a little more fun here," said Reyes, who lowered his ERA to 2.22 with the Indians. "I'm able to relax better. It feels like the pressure's off."
Asked what happened with the Cardinals, Reyes said, "I don't want to talk about that any more. I'm looking forward to this now. It's a great team and I'm having fun watching them."
With the game tied at 3, Ryan Garko led off the ninth with a single off Eddie Guardado (3-3). Pinch runner Andy Gonzalez advanced to second on Kelly Shoppach's sacrifice bunt, and Gonzalez raced home on Gutierrez's single up the middle.
Betancourt (3-4) pitched a perfect ninth for the win, but only after he and his bullpen mates couldn't hold Reyes' lead.
Texas tied the score with a two-run eighth inning. Gerald Laird's two-out RBI double off Juan Rincon made it 3-2, and the Rangers went on to load the bases before Betancourt came on and walked pinch hitter Ramon Vazquez.
The Rangers (63-68) lost for the 14th time in 17 games to fall five games under .500 for the first time since May 7.
Texas opened the scoring in the third inning on Milton Bradley's RBI single.
Cleveland came back with a two-run fourth against Texas starter Vicente Padilla on Shin-Soo Choo's RBI triple that skipped past Texas center fielder Josh Hamilton and Garko's sacrifice fly.
Hamilton took a bad angle on the ball, and the gaffe was costly.
"He tried to make a play," Rangers manager Ron Washington said. "The next time in that situation, he needs to leave his feet. He's learning."
Padilla hit David Dellucci with a bases-loaded pitch in the fifth to force in a run and stretch Cleveland's advantage to 3-1.
Padilla allowed three runs and five hits in five innings. He struck out eight, walked one and hit two batters.
The Rangers continue to struggle with a battered pitching staff and a lineup missing two injured run-producers, Ian Kinsler and David Murphy.
"When you look at all the injuries and adversity we've had to put up with, it might have caught up with us," Washington said.
All-Star shortstop Michael Young dismissed any alibis for the Rangers.
"We haven't played good baseball," he said. "Injuries aren't an excuse. Every team has them. We can go in two directions. We can pout or we can battle and make some good adjustments."
Bradley, who's been hobbled by a quad injury, was removed for a pinch runner in the eighth in what Washington termed a precautionary move. ... Grady Sizemore, one homer short of reaching 30 homers and 30 stolen bases for the 14th time in AL history, was the Indians' DH rather than taking his usual spot in center field. "We wanted to get him off his feet and out of the heat," manager Eric Wedge said. ... Hamilton, the major league RBI leader with 115, has had a breakthrough season, but there are still aspects of his game that Washington would like to see developed. For example, Washington would like Hamilton to walk more. He entered Sunday with 52 walks, 20 behind team leader Milton Bradley even though Bradley had played in 23 fewer games. ... Three Indians rehabbing from injuries - DH Travis Hafner, 2B Josh Barfield and C Victor Martinez - were in the lineup for Triple-A Buffalo on Sunday. The trio went a combined 2-for-9 in a 2-0 loss to Scranton, with singles by Barfield and Martinez.