CLEVELAND -- Scott Kazmir earned his first victory in three seasons, Nick Swisher homered in his first at-bat since missing three games with a sore shoulder and the Cleveland Indians beat Minnesota 7-3 Saturday for their sixth straight victory.

Kazmir (1-1), a two-time AL All-Star who pitched in an independent league last season, allowed two runs in six innings. It was his first win since beating Tampa Bay on Sept. 19, 2010, while with the Angels.

The left-hander, who allowed eight earned runs in 8 1/3 innings in his first two starts, struck out seven.

Swisher, who hadn't played since Monday, homered off Kevin Correia (3-2) in the first. Jason Kipnis, who had three hits, also homered in the inning and added an RBI single in the second.

Cleveland has won six straight for the first time since winning seven in a row April 26-May 3, 2011.

Rookie outfielder Aaron Hicks, the Twins' top prospect, hit his first major league home run to lead off the fifth, clearing the 19-foot wall in left field.

Kazmir on 53 games for the Rays from 2005-09 before his career his career was derailed by arm injuries. He was 9-15 for the Angels in 2010 and appeared in only one game in 2011 before being released.

Kazmir pitched for Sugar Land in the Atlantic League last season, going 3-6 with a 5.34 ERA in 14 games. He signed a minor league contract with the Indians in January.

Correia failed to go seven innings for the first time in six starts this season. The right-hander, who had won three consecutive starts, allowed four runs in five innings.

Kipnis, who has six RBIs in his last two games, and Swisher both homered to right in the first. Swisher, who entered the game in a 4-for-28 slump, missed the two-game series against Philadelphia and didn't play Friday.

The Twins scored in the second on Pedro Florimon's RBI single, but his misplay in the field helped the Indians add two in the bottom of the inning. After Michael Brantley's single gave Cleveland a 3-1 lead, Florimon was unable to catch Kipnis' popup that fell for a run-scoring single. The shortstop ranged into shallow left field, but the ball drifted away from him and dropped in.

Kipnis tripled in the seventh and scored on Asdrubal Cabrera's double. Mark Reynolds scored Cabrera with a two-out single.

Ryan Doumit's RBI single off Joe Smith in the eighth cut the lead to 6-3, but Chris Parmelee flied out with two on to end the inning. Ezequiel Carrera had an RBI single in the bottom of the inning.

Hicks, who is batting .123, homered on Kazmir's first pitch of the fifth. Joe Mauer had a hit and a walk in three at-bats and is in a 5-for-42 slump.

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