Willingham and Arcia, who both missed nearly two months with wrist injuries suffered the first week of the season, went a combined 1-for-7 with a hit by pitch. The Twins were held to two runs or fewer for their fifth straight game.
"It was another day where we didn't get it done offensively again," Twins manager Ron Gardenhire said. "We're happy to have a couple guys back, but right now we have to figure out a way to score a few runs to help out the pitching."
It was hard to cast too much blame on Correia, who just missed out on a quality start. He gave up four runs on seven hits -- with three of those runs coming with two outs -- to get pegged with the loss. It was just the third time in 10 starts this season he's gone at least seven innings.
"Kevin did a decent job," Gardenhire said. "But we had a couple innings where we didn't finish them off."
Correia gave up two early runs in the second as Alex Rios started the rally with a single before stealing second with one out. Chris Gimenez followed with a line drive that went off Correia's foot for an infield single to score Rios, as Correia's throw to first hit Gimenez to allow the Rangers catcher to reach second and Rios to score.
"I should've made a decent throw," Correia said. "I just rushed it. It just hit me in the bottom of my foot so it didn't affect it."
After Leonys Martin grounded out, Michael Choice followed with a double off the wall in right field to score Gimenez with two outs.
Correia settled down after Choice's double, retiring 10 straight batters until giving up a two-out single to Rougned Odor in the fifth. Odor seemed to be fooled by Correia's 1-2 curveball but was able to find the hole between first and second base for a single to keep the inning alive.
It proved to be important. Shin-Soo Choo followed with a single of his own before Elvis Andrus laced a two-run double to left field. Willingham, playing in his first game since April 6 after missing nearly two months with a small fracture in his left wrist, couldn't cut the ball off in the outfield and that allowed Choo to score all the way from first.
"The two-out hits were really big for us today," Rangers manager Ron Washington said. "Our guys did a really good job in those situations, stringing some good at-bats together. We just need to be more consistent at it."
It was enough for Rangers right-hander Nick Tepesch, who allowed two runs on seven hits over 6 2/3 innings to get his second win of the year.
The Twins scored early with a solo homer from Trevor Plouffe in the first inning, but saw a two-out triple from Oswaldo Arcia erased after a replay challenge from Washington. Arcia hit a routine fly ball to right field that dropped in between Rios and Martin. But Arcia was thrown out trying to advance to third on the play despite originally being ruled safe.
Minnesota scored again in the second on a bloop RBI single from Eduardo Escobar with two outs. But the Twins stranded two runners that inning as Brian Dozier popped out to third to end their scoring opportunity.
"The first couple of innings I was up in the zone and everything was flat," Tepesch said. "It was all about me making adjustments and getting the ball down. That was the big thing, forcing the ball down in the zone and pounding the zone."
The Twins went 1-for-6 with runners in scoring position to continue their recent struggles offensively. They scored just four combined runs over the weekend in a three-game sweep at the hands of the Giants.
The Rangers added three insurance runs with two outs in the eighth against reliever Jared Burton. Gimenez came through with a two-run double after the Twins decided to intentionally walk Rios with two outs. Gimenez then scored on an RBI single by Martin to right field.
Six of the seven runs scored by Texas came with two outs to help them pick up their third straight win and move above .500 for the first time since May 12.
"They're a hot baseball team over there," Gardenhire said. "They're scoring runs. And they did it again."