Seeking their first postseason appearance since 2007, the Indians (91-70) took a one-game lead over Tampa Bay and Texas (both 90-71).
Cleveland is assured of at least a tie for the AL wild card. With three teams seeking the two wild cards, Sunday's results could decide the matter or lead to one or two tiebreaker games at the start of next week.
Carlos Santana homered for the Indians, who have won 14 of their last 16.
If the three teams are tied after Sunday, Cleveland would host Tampa Bay on Monday, with the winner advancing to the postseason. The loser would play at Texas on Tuesday for the second wild card.
In the event Sunday ends with a tie for the second wild-card berth, there would be a one-game tiebreaker Monday. Tampa Bay would host Cleveland, Texas would be home against the Rays or the Indians would host the Rangers.
The two wild cards would then meet in a postseason game Wednesday to determine which advances to the division series.
After a rain delay of 2 hours, 26 minutes at the start, Kazmir (10-9) allowed one run and six hits in six innings, and Marc Rzepczynski, Cody Allen and Joe Smith each followed with an inning of hitless relief. Kazmir won his second straight start after going 1-5 with a 5.82 ERA in his previous seven outings. He is 3-0 against Minnesota this year with a 1.45 ERA.
Santana hit a two-run homer in the fourth, but Eric Fryer singled in a run in the bottom half. Michael Bourn had a two-run triple in the fifth and scored on Jason Kipnis' single for a 5-1 lead.
Hoping to make Minnesota's 2014 rotation, Cole De Vries (0-2) allowed five runs and six hits in five innings.
Minnesota has lost nine of 10, and Twins manager Ron Gardenhire will not win his 1,000th game this season. Gardenhire, who is not under contract for next year, is two victories shy.
NOTES: Cleveland is 20-6 in September, its first month of at least 20 wins since August 1995. ... Indians DH Jason Giambi left the game with left forearm cramping. He is day to day. ... Bourn returned after missing three games with a sprained right wrist. ... Minnesota C Josmil Pinto did not play after being hit on the right hand by a pitch Friday. He is expected to play Sunday. ... Cleveland's Ubaldo Jimenez (12-9) is scheduled to pitch Sunday against Minnesota's Scott Diamond (6-12).
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