Cleveland capped a 10-game, season-ending winning streak with a 5-1 victory over the Minnesota Twins that gave them a 92-70 record and ensured they would host the AL wild card playoff game on Wednesday.
Their opponent was still unknown as Sunday wins by the Rays and Rangers kept them deadlocked with 91-71 records and set up a do-or-die showdown in Texas on Monday.
Tampa Bay scored six runs in the first inning and then held on to defeat the Toronto Blue Jays 7-6, while the Rangers snapped a 2-2 tie in the sixth on their way to beating the Los Angeles Angels 6-2.
The winner of Monday's Rays-Rangers duel will advance to the one-game, wild card playoff in Cleveland on Wednesday to determine the fourth team for the American League Division Series, which will start on Friday. The Boston Red Sox, Oakland A's and Detroit Tigers are already qualified as division winners.
In the National League, the Pittsburgh Pirates (94-68) will host the Cincinnati Reds (90-72) at PNC Park on Tuesday in their wild card contest after completing a three-game sweep of their final regular season series in Cincinnati.
The National League's best-of-five Division Series which features division champions Atlanta Braves, St. Louis Cardinals and Los Angeles Dodgers, will begin on Thursday.