Nick Swisher homered in the first inning for the Indians, who became the first major league team to win its final 10 regular-season games since the 1971 Baltimore Orioles finished with 11 straight victories, according to STATS.
Cleveland will host Tampa Bay or Texas in the one-game AL wild-card playoff on Wednesday night. The Rays and Rangers are playing a tiebreaker on Monday.
Jimenez (13-9) gave up one run and five hits in 6 2-3 innings for the Indians, who became the first team to sweep seven four-game series in one regular season since the 1943 St. Louis Cardinals. After the final out, Cleveland players mobbed each other on the diamond in a jubilant celebration.
Scott Diamond (6-13) gave up four runs — two earned — and seven hits for the Twins (66-96).
RANGERS 6, ANGELS 2
ARLINGTON, Texas (AP) —Texas forced a one-game tiebreaker for the second AL wild-card spot, winning its seventh straight when Geovany Soto hit a tiebreaking RBI double and later homered to beat Los Angeles.
The Rangers (91-71) added game No. 163 to the regular season, and will host Tampa Bay on Monday night. The winner plays two days later at wild-card leader Cleveland in another win-or-be-done matchup.
About the same time Tampa Bay wrapped up its 7-6 win at Toronto to necessitate a victory by the Rangers to keep playing, Craig Gentry hit a two-run single in the fifth for a 2-1 lead.
Los Angeles quickly tied the game against major league strikeout leader Yu Darvish in the sixth, but the Rangers went ahead to stay in the bottom half on Soto's two-out double.
Adrian Beltre and Soto added solo homers in the eighth.
RAYS 7, BLUE JAYS 6
TORONTO (AP) — Evan Longoria and Tampa Bay assured the Rays would tie for an AL wild-card berth, scoring six runs in the first inning and then holding off Toronto.
Tampa Bay and the Rangers, who beat the Angels, tied for the second wild-card spot. They will play Monday night in Texas to decide who faces Cleveland in the wild-card game Wednesday.
Longoria hit an RBI double as the Rays used their highest-scoring first inning since 2010 to go ahead early. Tampa Bay took a 7-0 lead into the sixth before Toronto rallied.
Rays manager Joe Maddon was ejected in the seventh and the Blue Jays put the go-ahead run at the plate in the eighth and ninth innings. Fernando Rodney got four shaky outs for his 37th save in 45 chances.
ORIOLES 7, RED SOX 6
BALTIMORE (AP) — Ryan Flaherty had two hits subbing for Chris Davis after baseball's home run champ left with a sprained wrist, and Baltimore wrapped up its season with a victory over playoff-bound Boston.
Flaherty hit an RBI single in a five-run fifth and a run-scoring double when the Orioles took the lead for good in the sixth.
Davis was hurt in the fourth inning when his arm got in the way of Jacoby Ellsbury on a play at first. The player who accepted the Orioles' MVP award before the game walked off to a standing ovation, finishing tops in the majors in both homers (53) and RBIs (138).
The Orioles finished 85-77, giving them back-to-back winning seasons for the first time since 1996-97.
The Red Sox finished up 97-65, tied with the St. Louis Cardinals for the best record in baseball. Boston will open its division series at Fenway Park on Friday against the winner of the AL's wild-card playoff.
YANKEES 5, ASTROS 1, 14 INNNIGS
HOUSTON (AP) — Mark Reynolds hit a tiebreaking homer in a four-run 14th inning, and New York went into an off-season of uncertainty with a victory over Houston, whose 15-game losing streak was the longest at the end of the season in more than a century.
Mariano Rivera didn't pitch in the final game of a career that started in 1995, and Robinson Cano and Curtis Granderson were among the players unsure whether they had played their final games for the Yankees (85-77).
Bothered by sore legs, Alex Rodriguez also didn't get into the game. The appeal of his 211-game drug suspension starts Monday.
New York finished with its fewest wins in a non-strike season since 1992 and failed to make the playoffs for only the second time in 19 years. Manager Joe Girardi's contract is expiring, and he hasn't said whether he wants to come back for a seventh season.
Houston (51-111) set a team record for losses and had the most in the majors since Arizona lost the same number in 2004. The Astros finished with the lengthiest season-ending losing streak since the 1899 Cleveland Spiders dropped their last 16, according to STATS.
ROYALS 4, WHITE SOX 1
CHICAGO (AP) — Bruce Chen pitched four-hit ball into the seventh inning and Kansas City beat Chicago to finish off its best season in 24 years.
Kansas City won three of four in Chicago and went 17-10 in September for its most successful month of the season. The Royals' 86-76 record was their best mark since they went 92-70 in 1989.
Chen's sharp outing put a damper on what might have been the final major league game for White Sox captain Paul Konerko, who is eligible for free agency and isn't sure if he will play again next year. The veteran first baseman is second in franchise history with 427 homers and 1,361 RBIs, and third with 2,249 hits.
Chen (9-4) allowed one run, struck out four and walked three in 6 2-3 innings.
Jose Quintana (9-7) pitched seven innings to reach 200 for the season. He was charged with four runs and six hits.
ATHLETICS 9, MARINERS 0
SEATTLE (AP) — Sonny Gray threw five shutout innings and Oakland had a pair of four-run innings to close out the regular season with a win over Seattle in Eric Wedge's final game as Mariners manager.
The A's now turn their attention to the AL Division Series against Detroit that will begin Friday in Oakland, while Seattle (71-91) enters the off-season with another managerial search on the docket after a 12th straight season without the making the playoffs.
Oakland gave a few of its starters the finale off, while some others made cameos before getting a rest before beginning the post-season.
Chris Young got Oakland started with a two-run single in the second, followed by RBI doubles by Seth Smith and Brandon Moss. Alberto Callaspo had an RBI single in the fifth, followed by an RBI double from Josh Reddick and a two-run single by Daric Barton.
Gray (5-3) struck out eight and gave up three hits.
Oakland finished with 96 wins, its most since reaching that total in 2003.