Arcia misjudged a deep fly to the warning track off the bat of Victor Martinez with one out in the ninth, and the drop allowed Torii Hunter, the eventual winning run, to reach third.
"I tried to get back to the wall, but I messed up," Arcia said after the game through his translator, bullpen coach Bobby Cuellar. "I was short of the wall and missed the ball."
It was the most damaging of two crucial mistakes made by Arcia on Sunday.
"I've been there," Hunter said. "Even when I was with the other team, that's the way it was. Even in center field, you get bad jumps."
In the first inning, Minnesota starter Ricky Nolasco ran into a jam with one on and two outs. He appeared to navigate successfully out of it when he induced a fly ball off the bat of Victor Martinez. Arcia never had a chance at the ball, which he lost in the midday Comerica Park sun, giving the Tigers an early lead for the second straight day.
"Arcia didn't see the ball," said Twins manager Ron Gardenhire. "That was obvious. He had no clue where the ball went. It was obviously a tough sun field out there, bright. If you can't see the ball, you can't see the ball."
Nolasco lasted 5 1/3 innings and allowed three runs on nine hits.
"He's a veteran. He can get out of those things, but eventually it's going to get to you," Gardenhire said.
Detroit added a run in the second on a sacrifice fly, but Minnesota scored three in the sixth to take the lead.
Tigers starter Rick Porcello had sat down eight straight before Joe Mauer hit a ground-rule double into the seats down the left-field foul line. Josh Willingham doubled him home before tying the score on a single by Kendrys Morales.
Kurt Suzuki singled in Morales for the third run of the inning when catcher Alex Avila couldn't handle J.D. Martinez's throw from left on a play at the plate.
None of the offense came from Brian Dozier, who was inserted into the lineup for the first time since injuring his back earlier in the week in Toronto. In his lone at-bat after entering as a defensive replacement on Saturday, he hit a ninth-inning homer. Dozier batted third for the first time this season on Sunday.
"We're just trying to figure out how to score runs," Gardenhire said. "Joe [Mauer] had a couple good at-bats in the two-hole. We're just trying to figure out what works. We're just mixing and matching and doing the best we can."
Detroit responded with a run in the bottom of the sixth, taking the wind right out of the Twins' sails following their big inning.
"It's tough once you get a lead like that," Gardenhire said. "You're looking for a shutdown inning, and we didn't get it."
Gardenhire made a bold maneuver later in the sixth inning to try and prevent further damage.
He called for an intentional walk of Avila to get to Detroit's hot rookie, Eugenio Suarez. The decision paid off, as reliever Jared Burton retired Suarez and Ian Kinsler to end the threat.
"Burton did a good job of coming in and holding them down right there," Nolasco said.
Two ninth-inning singles off former Twins closer Joe Nathan went to waste, and Detroit turned right around and won the series in dramatic fashion on the walk-off sacrifice fly. It didn't go unprotested, as the Twins appealed that Hunter left third base before the ball was caught.
"Everybody was screaming out of the dugout," Gardenhire said. "That's a normal thing in baseball. 'You left too early.' It's havoc out there, and who knows what the hell can happen? You might get lucky."
Luck, however, wasn't on the Twins' side on Sunday.
Minnesota won't get another shot at Detroit, which they trail by five games in the division, until late August.