MINNEAPOLIS (AP) — Alexi Casilla singled home the winning run with one out in the 12th inning and the Minnesota Twins rallied past Detroit 6-5 in the AL Central tiebreaker Tuesday night, completing a colossal collapse for the Tigers.

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

Baseball’s only real pennant race this season needed an extra game, and extra innings to finish off a thriller that got better with every pitch.

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.

Detroit thought it had taken the lead in the 12th. But with the bases loaded, plate umpire Randy Marsh ruled that Brandon Inge was not hit by a pitch by Bobby Keppel. The replay appeared to show the pitch grazing Inge’s billowing uniform.

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 also started to scramble — they had 21 hours to get ready for Game 1 of the AL playoffs at Yankee Stadium against New York ace CC Sabathia.

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

It was the first AL tiebreaker to go to extra innings, and made up for Minnesota’s disappointment last October when it lost 1-0 in Chicago to the White Sox in an AL Central tiebreaker.

Had the Twins lost, it would’ve been the final baseball game at the Metrodome. Instead, the Twins get the Yankees — New York was 7-0 against Minnesota this season.

‘‘We’re not going to have to face questions like ’Can you beat them?’ like we’ve had to answer during the course of the year,’’ Yankees manager Joe Girardi said. ‘‘Once the playoffs start though, it’s a new series and we know the importance of each game. You can pretty much throw everything else out the window.’’

A day after Brett Favre and the Minnesota Vikings beat the Green Bay Packers at the Dome — ‘‘Monday Night Football’’ is what delayed this tiebreaker for a day — the Twins pulled off a Tuesday Night Thriller.

Tigers reliever Fernando Rodney (2-5) worked his longest appearance of the season, getting the last two outs of the ninth. He gave up a single to Gomez to start the 12th, and the speedy center fielder — who came in for defense late in the game — moved up on a groundout. He came racing around for the winning run when Casilla’s single made it through the right side of the infield.

The Twins rushed out of the dugout in celebration even before Gomez reached the plate. Their comeback from a seven-game gap with 20 to play was complete.

Joe Mauer, who heard thunderous ‘‘M-V-P!’’ chants from the largest regular-season baseball crowd in Metrodome history throughout the game, led his team on a sprint around the warning track as they slapped hands with fans in the first rows.

The Twins got nipped by the White Sox in Game 163 last year, but this struggle for the division on the last possible day was even more dramatic with all kinds of chances for either team to take it.

There will be no rest for the winners, though: The Yankees predictably picked Wednesday to start their series, with Game 2 scheduled for Friday. Both managers played down the potential disadvantage before the game, but whichever team emerged from this was going to be drained. Ron Gardenhire and Jim Leyland made so many moves for defense and relief that the lineups and pitching staffs were depleted by the end.

Keppel, Minnesota’s eighth pitcher, loaded the bases with one out in the 12th. His first pitch to Inge appeared to brush his jersey, but it was simply called a ball by Marsh. Inge seemed ready to take his base and Leyland came out to discuss the call with Marsh.

Second baseman Nick Punto then scooped Inge’s grounder and fired home in time to get the runner on the force, and Keppel struck out Gerald Laird to squelch that rally.

Twins closer Joe Nathan found trouble in the ninth when consecutive singles put runners at the corners, but he got a strikeout and a line-drive double play to end that threat. The four-time All-Star gave two huge pumps of his right arm as he spun to thank his defense and run to the dugout, preserving the tie.

Inge’s two-out double in the 10th gave the Tigers a 5-4 lead, but Michael Cuddyer sliced a triple past Raburn in left and scored on Matt Tolbert’s bouncing single through the middle in the bottom of the inning.

On the potential winning sacrifice fly, though, Casilla strayed a bit too far from third and was thrown out by Raburn trying to score to end the inning. The split-second Casilla needed to retouch the base might have cost him the run.

He more than made up for that mistake later.

According to sports researcher STATS LLC, only three teams since 1901 have blown a three-game lead in the standings with four games left. The Houston Astros lost three straight games to Los Angeles in 1980, but they recovered to defeat the Dodgers in a tiebreaker game for the NL West. The Milwaukee Brewers lost three in a row to Baltimore in 1982 to force a tie, but they beat the Orioles in the final regular season game to win the AL East.

After splitting four in Detroit last week — a loss in the series finale Thursday would’ve wrapped up the division for the Tigers — the Twins came home for the final scheduled series in the bubble needing a sweep of the Kansas City Royals and did just that.

So with 54,088 fans in attendance, the place was erupting with noise and excitement. The chants for Mauer, who wrapped up his third batting title, were deafening. Leyland even told his players before the game to think of the loudest experience of their life and multiply it by four to anticipate the decibel level for this game. Dome ball came in handy again, on a day when the city was drenched by cold rain.

Rookie starter Rick Porcello pitched well beyond his 20 years for the Tigers, and Miguel Cabrera made up for a miserable weekend — on and off the field — with a two-run homer against Scott Baker in the third inning that made it 3-0. The crowd chanted ‘‘al-co-ho-lic’’ right before Cabrera went deep, a rude reference to the first baseman’s fight with his wife after he came home late and drunk.

The Twins crept back, though, and Orlando Cabrera’s two-run homer in the seventh gave them a brief lead that Magglio Ordonez ended with his leadoff homer in the eighth.

NOTES: This was the ninth tiebreaker game in baseball history, and the third straight year with a 163rd game. Only two of them went to extra innings. … Seven members of the Metrodome’s cleaning and maintenance crews were honored on the mound before the game for the work of those groups in converting the field back and forth from baseball to football in light of Monday’s Packers-Vikings game.