Eduardo Escobar also homered and drove in three runs, helping the Twins bail Kyle Gibson out of a 3-0 deficit after an RBI triple by Alex Presley and a two-run home run by Nicholas Castellanos.
Gibson was removed after 4 2/3 innings, so Jose Berrios (14-8) was credited with the win after recording four outs in a tuneup relief outing. Matt Belisle notched his ninth save with a perfect ninth inning for the Twins, who will visit New York or Boston on Tuesday in the AL wild-card game.
Dozier opened the Minnesota first with a double against Matt Boyd (6-11) that would have been a triple had Dozier not tripped after rounding second. He hustled to dive head first back into the base and avoid an out, climbing to his feet with a wide grin on his face as the rest of the team razzed him from the dugout.
He then scored on Escobar's double, trimming Detroit's lead to 3-1.
Not to be outdone in the field, Dozier made a diving stop of Presley's sharp grounder to second base with two runners in scoring position to end the second inning for Gibson, likely saving two runs.
With video clips of champagne celebrations from seasons past concluding with the party in the clubhouse at Cleveland on Wednesday, when the Twins learned they became the first team to go from 100-plus losses to the playoffs in one year, the crowd of 34,580 had plenty to appreciate. They saved some of their loudest cheers for Miguel Sano, who pinch-hit in the seventh inning and grounded out in his first appearance since fouling a ball off his left shin bone on Aug. 19.
Dozier and Escobar went deep back to back in the second, right after Ehire Adrianza nearly hit one out but settled for a double. Dozier is 13 for 30 with three homers and five RBIs in his career against Boyd.
Since signaling the end of their contention with the current group through summer trades that jettisoned veterans J.D. Martinez, Alex Avila, Justin Upton and Justin Verlander, the Tigers have predictably fallen hard during the final month of the schedule. They've been outscored 190-103 in September for a 5-23 record.
Castellanos, who has a career-high 26 home runs, became the 10th player age 25 or younger in Tigers history to top 100 RBIs. Miguel Cabrera was the last one to do so, in 2008. In 28 games this September, Castellanos, the team's first-round draft pick in 2010, is batting .373 (41 for 110) with seven homers and 25 RBIs.
Escobar has quietly been one of the most valuable players for the Twins down the stretch, taking over as the everyday third baseman after Sano was hurt. Escobar has career highs with 21 home runs and 73 RBIs, remarkable totals for a 5-foot-10, 185-pound utility player.
"He does let it fly," manager Paul Molitor said. "Sometimes I think he starts to swing before he knows what's coming, but he adjusts pretty well to the ball in flight, maybe better than most people."
Tigers: 3B Jeimer Candelario was back in the lineup after missing the game on Thursday with a sore left wrist. He struck out in his first three at-bats.
Twins: Sano came off the DL before the game, putting him in position for postseason action. Molitor did not commit to including him on the wild-card roster.
Tigers: RHP Buck Farmer (4-5, 7.12 ERA) will pitch the middle game of the series. He is 1-4 with an 8.69 ERA in five starts this month.
Twins: RHP Aaron Slegers (0-0, 7.36 ERA) will make his third major league start on Saturday night, with RHP Bartolo Colon likely to take his turn on Sunday.