Rick Porcello (3-1) gave up four runs and six hits with four strikeouts in five-plus innings for the Tigers, who broke the game open with seven runs in the third. Rajai Davis had three hits to raise his average to .354.
Chris Colabello drove in his 27th run for the Twins, setting a franchise record for RBIs in April.
Jason Kubel had two doubles among his three hits for the Twins. Brian Dozier hit his seventh homer of the season and Kurt Suzuki drove in two runs, giving him 19 RBIs on the season, which leads all catchers.
Correia served up a two-run homer to Castellanos in the second - and probably only got through that inning thanks to a poor decision by third base coach Dave Clark to send slow-footed Alex Avila from first base on a double by Andrew Romine. Avila was thrown out at home and Ian Kinsler grounded out to short-circuit the rally.
But the Tigers had more in store for Correia.
Hunter led off the third with a double and, after Miguel Cabrera's groundout, the next five batters reached base with three hits and two walks, the last one from Romine with the bases loaded to make it 5-1. Hunter added a two-run single off Anthony Swarzak later in the inning that pushed the lead to 9-1.
There are no statements delivered in April, but the Tigers did throw a little cold water on what has been a surprising start to the season for the Twins. Minnesota has lost at least 96 games in each of the past three years, but rode the second-highest scoring offense in the American League to an 11-10 start that put the Twins right on heavily favored Detroit's heels in the AL Central.
After breezing through the first five innings, Porcello didn't get an out in the sixth before being lifted for Justin Miller. Tigers manager Brad Ausmus had to use five more pitchers to finish the game, but that big third inning gave his team plenty of cushion to absorb a four-run sixth by the Twins.
NOTES: Twins GM Terry Ryan finished his last round of radiation treatment for cancer, assistant GM Rob Antony said. Ryan is expected to return to Target Field this weekend. ... Avila left the game with a bruised left shin and is day to day. ... Twins OF Oswaldo Arcia was scheduled to fly to Triple-A Rochester on Saturday to start a rehab assignment. Arcia has been on the disabled list since April 5 with a wrist injury. ... RHP Anibal Sanchez (0-2, 3.54 ERA) pitches for Detroit on Saturday against RHP Phil Hughes (1-1, 6.43).