Santana (13-7) left with a broken nail and blister on his left middle finger, but would not use it as an excuse for giving up four runs in only five innings.
"They are a hot team and I didn't get the job done," said Santana, adding that he may not throw his next bullpen session in order to give the injury time to heal before his next start.
"I'm all right. It's been like this for a few weeks."
The Twins also lost catcher Joe Mauer with a bruised right shoulder.
"It didn't feel too good and every inning after it kept getting worse," said Mauer, who was hit by a foul tip in the fourth inning and left in the seventh.
The Indians stretched their winning streak to five games and have moved 6½ games ahead of Minnesota by going 16-5 since Aug. 18. They are a half-game ahead of the New York Yankees.
Westbrook (14-14) said he spent a lot of time thinking about trying to keep his team atop the wild-card scramble while facing Santana.
"I was fired up," said the usually low-key right-hander. "You can't give up too many runs against a pitcher like him. The defense was tremendous and the offense came through, too."
Cleveland turned a key double play in the fourth and second baseman Ronnie Belliard ended the sixth by ranging behind the bag to get a sharp grounder hit by Juan Castro, then throwing off-balance to get the runner at first -- ending up sprawled in short left field.
Grady Sizemore led off the first with a homer off Santana, who came in 5-0 with a 2.84 ERA in 18 career games against Cleveland.
"That got me even more pumped up," said Westbrook, who allowed two runs and six hits over six innings. He won for the fourth time in five starts and is 13-7 since a 1-7 start.
Cleveland snapped a 2-all tie with a two-run fifth.
Casey Blake hit a leadoff double and scored on a one-out double by Coco Crisp. Jhonny Peralta walked, and one out later Victor Martinez singled to left to score Crisp -- but Peralta was out trying for third to end the inning.
It was the second time the Indians' young shortstop thwarted a rally while trying to advance.
Sizemore hit an 0-2 pitch over the wall in right for his 18th homer in the first -- just the fifth homer by a left-hander off Santana this year. Crisp then singled and scored on a double by Peralta, who was out trying for a triple.
It was just Peralta's second hit in his last 29 at-bats, and his first in 15 career at-bats against Santana.
The four runs over five innings were the most allowed by Santana in 12 starts since July 6. He lost for the first time since Aug. 1 against Oakland.
In his previous start against Cleveland on Sept. 3, he struck out 10 without a walk, giving up only two hits and one run over eight innings in a no-decision.
"We didn't swing at his changeup this time," Crisp said. "We tried to be more aggressive and scored just enough. Four runs isn't dominating anyone. He's still one of the best."
The Twins scrapped back with single runs in the second and fourth to tie it.
Jacque Jones opened the second with a bloop single to left and stole second. Two outs later, Castro grounded a single through the middle to make it 2-1.
In the fourth, Jones hit a leadoff double and took third when Blake bobbled the ball in the right-field corner for an error. Matt LeCroy followed with an RBI single to center.
Before the game, Gardenhire acknowledged the importance of the three-game series for his three-time defending AL Central champions.
"It's not a must-sweep, but this game is must-win for us," he said. "And then the game Saturday night is must-win and the game Sunday is must-win."
Afterward, he admitted it was a crushing loss.
"We had our best pitcher going tonight and you've got to win," he said. "All we can do is try to come back tomorrow."
- Santana is 24-6 in his last 36 road starts.
- Westbrook had six assists -- the most by an Indians pitcher since John Denny had six on April 20, 1981, against Kansas City.
- The Twins have totaled five runs in Santana's last four starts.
- Plate umpire Andy Fletcher was shaken, but stayed in the game when a foul ball by Twins OF Lew Ford glanced his mask in the eighth inning.