MINNEAPOLIS — Baseball’s only real pennant race needed an extra game and extra innings to finish off an AL Central thriller that got better with every pitch.

Alexi Casilla singled home the winning run with one out in the 12th and the Minnesota Twins rallied past Detroit 6-5 in their tiebreaker Tuesday night, completing a colossal collapse for the Tigers.

‘‘This is the most unbelievable game I’ve ever played or seen,’’ Twins shortstop Orlando Cabrera said.

As Carlos Gomez streaked home from second with the winning run — well ahead of a late throw from right field — Homer Hankies spiraled around the Metrodome. The Twins celebrated and scrambled — they had 21 hours to get ready for Game 1 of the AL playoffs at Yankee Stadium against New York ace CC Sabathia.

The Tigers became the first team in major league history to blow a three-game lead with four games left.

‘‘I guess it’s fitting to say there was a loser in this game because we lost the game, but it’s hard for me to believe there as a loser in this game,’’ Tigers manager Jim Leyland said. ‘‘Both teams played their hearts out. You can’t ask for anything more than that.’’

The Twins overcame a seven-game gap in the final month, went 17-4 to pull even on the final weekend and won their fifth division title in eight years.

‘‘We just feel like we have nothing to lose, man,’’ outfielder Denard Span said.

Both team had their chances to end it earlier, and each club scored in the 10th. Casilla was thrown out at the plate to end that inning by left fielder Ryan Raburn after tagging up.