Cleveland surpassed its goals.
The Indians started the series trailing Detroit by a half-game. They traveled to Boston in first place by a season-high 2½-games.
"You work hard to try to win a series, but when you are coming in here you don't expect anything beyond that," Cleveland manager Eric Wedge said. "We came out on top this time, but it's not going to be any easier when they come in next weekend."
The AL Central powers have 15 more scheduled games this season, including a four-game series that starts Thursday night in Cleveland.
"They're very comparable to us, but they got the best of us this series," Detroit first baseman Sean Casey said.
Cleveland (31-17) has its best record after 48 games since reaching the same mark at this point in 2001, the last time it won the division and played in the postseason. Since starting 7-7, the Indians have won 24 of 34.
The defending AL champion-Tigers were swept for the first time this season.
"It doesn't bother me a bit. It's May," Detroit manager Jim Leyland said. "They've got a good team and we've got a good team."
Garko's home run gave the Indians a 4-0 lead, and Blake's homer put them ahead 5-3.
"They are the defending champs and they've got All-Stars all over the place, so any time you sweep these guys, especially on the road, it is big," Garko said. "But it is still early, and we've got well over 100 games left, so you don't know how big this might turn out to be."
Fausto Carmona (6-1) gave up three runs and nine hits over seven innings. He hasn't lost or given up more than three runs since dropping his first start this season.
"He has heavy sink and he throws it hard. That's why he's off to such a good start," Casey said. "We had some opportunities, but he shut the door. When you have the sink that he has, it's tough to get it up in the air."
Mike Maroth (3-2) allowed five runs and six hits in eight innings, losing consecutive starts after going 3-0 in his first seven.
"It looked like it could be a rough one," Leyland said. "But he settled in and did a good job of giving us quality innings and a shot."
Craig Monroe, Gary Sheffield and Magglio Ordonez hit three straight RBI singles in the third to pull Detroit within a run, then Carmona pitched out of one of his jams. With two on and one out, Carmona got Carlos Guillen to line out and Ivan Rodriguez to strike out.
The Tigers had two on and no outs in the sixth and Carmona didn't let them have anything to show for it, getting a double play and a line out.
Brandon Inge led off the seventh against Carmona with a double, ending an 0-for-16 streak, and Sheffield hit a two-out single, but both were stranded after the hot-hitting Ordonez grounded out.
The Tigers had 11 hits, but scored just three runs because they left nine runners on base.
"We had them out there all night, we just couldn't get them in with a big hit," Leyland said.
- Tigers 2B Placido Polanco (strained oblique) was out of the lineup, but is expected to play Monday night at Tampa Bay.
- Indians RHP Jake Westbrook (abdominal strain) threw in the bullpen before the game and is scheduled to pitch a simulated game Tuesday in Boston.
- The Tigers' only other three-game losing streak came against Kansas City and the White Sox from April 18-21.
- Carmona had lost 11 straight decisions until winning on April 24.
- Maroth matched a season high with five walks.
- Cleveland is 13-4 in AL Central games after going 35-40 in the division last year.
- The Indians have at least a homer in a season-high 11 games.
- Garko is hitting .390 with five homers and 15 RBI this month.
- Cleveland swept the Tigers in a three-game series for the first time since Aug. 5-7, 2005.