Tommy Milone allowed four runs in the first inning of a 5-4 loss on Monday night.
"They put a 4-spot against him right out of the chute, which is a tough mountain to climb when you're facing a guy like David Price," Twins manager Paul Molitor said. "I thought our bats today against him were a lot better than the opener. We kept pecking away."
Danny Santana had two hits and an RBI for the Twins (8-11), who had the tying run at second base with one out. Milone (2-1) gave up five runs on eight hits in four innings.
The Tigers jumped on Milone early, with Jose Iglesias hitting a solo homer and Cespedes adding a three-run shot for a quick 4-0 lead.
"I've seen him mash balls like he did today in that first inning all too often," said Milone, a former teammate of Cespedes in Oakland. "It's not a good feeling to be on the other side of it. Good lineup, wish I could have some pitches back. Reality is I just couldn't get it done today."
Price had was one out away from a shutout in the season-opener against the Twins in Detroit.
Despite seven strikeouts in six innings and his fastball occasionally hitting 97 mph on the Target Field radar gun, Price said he was far from sharp.
"I guess I pitched good enough to get by," Price said. "But I can get better."
Price allowed three runs and his night ended on an RBI-double from light-hitting Jordan Schafer in the seventh that cut Detroit's lead to 5-3.
Joe Mauer hit his 313th double, moving him past Kent Hrbek and into sole possession of third place on the Twins career list. Mauer came around to score in the eighth, but Minnesota left a runner on second base with one out in the ninth against Soria.
"It was an uphill battle from the get-go," Twins second baseman Brian Dozier said. "But at the same time, good offensive teams, good teams in general, find ways to come back and win, and see what happens. They caught a few more breaks at the end than we did."
Twins shortstop Danny Santana had struggled at the plate and in the field in his follow up to his dazzling 2014 rookie season. Santana entered Monday with a .210 average and five errors. He had two hits, an RBI and a run scored and also turned two double plays.
"I think he's learning to separate offense and defense," Molitor said.
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.