Jose Iglesias raised his average to .397 with a homer and a triple among his three hits and Price (2-1) gave up three runs on six hits and struck out seven in six innings for the Tigers (14-6), who have won three straight after a four-game losing skid. Joakim Soria picked up his eighth save in eight chances.
The Tigers jumped on Milone early, with Iglesias hitting a solo homer and Cespedes adding a three-run shot for a quick 4-0 lead.
With that much of a cushion, Price didn't hesitate to attack the strike zone with that 97-mph fastball. He was tagged for eight runs in 2 1/3 innings the last time out against the Yankees and, after an overpowering start, couldn't quite put away the pesky Twins.
Price's night ended on an RBI-double from light-hitting Jordan Schafer in the seventh that cut Detroit's lead to 5-3.
Iglesias missed all of last season with stress fractures in both shins. He's been a difference maker early in this season, having hit safely in 15 of his 19 games and driving in the winning run to beat the White Sox on Friday.
Joe Mauer hit his 313th double, moving him past Kent Hrbek and into sole possession of third place on the Twins career list.
Tigers: Manager Brad Ausmus said RHP Justin Verlander's strained right triceps is making incremental improvement. Verlander started the season on the disabled list and had an MRI on Friday that showed a smaller amount of inflammation. He will have another MRI next week. "This is just one of those things you can't try to force your way through, which is hard because everything I've done in the past is, `Alright, let's attack this. Let's work through it. Let's go throw," Verlander said. "And this is just not one of those things you can do that with."
Twins: RHP Ricky Nolasco arrived in the Twin Cities after throwing 66 pitches in a rehab start. Manager Paul Molitor said the team wanted to evaluate his right elbow, but would not make a decision on the next step until later in the week. ... RHP Trevor May threw a bullpen without any issue after he was hit by a batted ball on Saturday.
The Tigers send RHP Anibal Sanchez (1-2, 5.96) to the mound to face RHP Mike Pelfrey (1-0, 2.65). Pelfrey threw seven shutout innings against Kansas City in his last start, his first scoreless outing in 23 appearances. The Tigers are 1/3 in games started by Sanchez this season and 13-3 in games started by anyone else.