MINNEAPOLIS -- Not too long ago, Johan Santana winning at the Metrodome was as close to a sure thing as there was in baseball.
Not this season. Santana has a new streak at the Dome, and it's not a good one.
Santana (3-2) was making his first home start since Tampa Bay snapped his remarkable regular-season winning streak on April 13. Santana was 17-0, and the Twins were 24-0, in his previous 24 home regular-season starts before he was outdueled by Scott Kazmir in a 4-2 loss.
"I don't really think about it," Santana said. "It's going to happen. ... I don't really think about winning and losing the game here. I'm just trying to do my job and hope that everybody else will step up and try to win the game."
The two-time Cy Young winner wasn't bad against Cleveland on Tuesday night, giving up four runs on six hits and striking out seven in seven innings. But he didn't get much help from a lethargic offense that was befuddled by Carmona (1-1).
The Dominican right-hander gave up two runs on six hits in 7 2/3 innings to snap a skid of 11 consecutive lost decisions, giving him his first victory since making his major league debut on April 15, 2006.
"Fausto was fantastic tonight," manager Eric Wedge said. "Fausto commanded both sides of the plate, used all his pitches, and really made some big pitches to good hitters when he needed to."
Joe Borowski allowed an RBI single to Jason Kubel in the ninth before finishing for his eighth save.
Travis Hafner homered in the first inning for Cleveland, which was coming off a 12-inning victory over the Twins on Monday night.
After giving up an RBI-double to Casey Blake in the seventh that made the score 4-2, Santana hit Hafner in the middle of the back on the first pitch of the next at-bat, prompting a conversation with plate umpire Jim Reynolds.
"Trying to throw a two-seamer inside and it went too far," Santana said. "It's not like I was trying to hit him or anything. It's part of the game. I play the game the right way."
Things were much less frustrating for Carmona, who breezed through the Twins' lineup.
Coming in, Carmona was closing in on the Indians' club record for consecutive losses. Guy Morton (1914) and Rod Nichols (1989-91) both lost 13 decisions in a row.
Carmona looked as though he might end the streak his last time out, when he gave up two runs on six hits in six innings and left with a 5-2 lead over the New York Yankees. But the Bombers scored six runs off Cleveland relievers, including Alex Rodriguez's three-run homer in the ninth.
The Twins didn't show nearly as much fight. They scored two runs in the fourth on an RBI single from Justin Morneau and a sacrifice fly by Torii Hunter to cut Cleveland's lead to 3-2, but Carmona settled down and retired the next nine hitters.
"He knew that Santana was pitching but he wasn't thinking about Santana," said first base coach Luis Rivera, acting as Carmona's interpreter. "He was thinking about being aggressive, going after the hitters and doing his job."
Santana has historically been a slow starter. It usually takes him about a month or so to sharpen his trademark changeup. He hit two batters Tuesday night and gave up at least one hit in the last four innings he pitched.
He struck out the first two batters he faced before giving up a homer to Hafner that traveled an estimated 431 feet to the deepest part of the Metrodome in right-center field.
Ryan Garko doubled and scored on a sacrifice from Jason Michaels in the Tribe's two-run fourth for a 3-0 lead.
"Johan's been the best pitcher in baseball the last three years," Twins catcher Joe Mauer said. "We're not worried about him."
Kubel's double in the third inning gave the Twins a two-base hit in 15 consecutive games. ... Santana made his 147th career start for the Twins, passing Joe Mays for 12th in franchise history. ... Indians SS Mike Rouse snapped an 0-for-15 to start the season with an RBI single in the eighth off Matt Guerrier.