MINNEAPOLIS -- For eight innings on Sunday afternoon, the Twins looked dead in the water. All of their season-long bugaboos -- the strikeouts, the stranded runners, the lack of situational hitting -- were conspiring to send the team to its eighth shutout loss of the season.

Then the Pink Eye Brigade gave Minnesota a jolt.

Willi Castro delivered a key pinch-hit RBI double as the Twins rallied for three runs in the ninth off White Sox closer Kendall Graveman to force extra innings. Then, after Chicago regained the lead in the 10th, Joey Gallo used his feet and his head to score on a short sacrifice fly to tie the game again.

It all led up to Ryan Jeffers’ game-winning RBI single with two outs in the 12th inning to help the Twins complete a sweep of the White Sox with a wild 5-4 victory at Target Field.

Minnesota played short-handed in the first two games of the series as Castro and Gallo had to be scratched from Friday’s lineup with cases of conjunctivitis. Both missed Saturday’s game as well, but they arrived at Target Field on Sunday hoping to make some type of contribution.

“Yeah, pink eye can’t hold these guys down,” said Twins manager Rocco Baldelli, who used his entire bench in piecing together the victory. “It’s good to get those guys back out there.”

Castro’s big moment came after Matt Wallner walked and Jeffers singled to lead off the ninth. Baldelli sent him to the plate for Michael A. Taylor, who had struck out in all three of his at-bats. Castro lined a double into the left-center gap that scored Wallner and moved Jeffers to third.

“There were two men on base. I just wanted to get one in,” Castro said. “I just think when you’re patient and you just go out there and just get the pitch that you want to hit, that’s the result.”

Carlos Correa followed with a sacrifice fly to make it 3-2, but Castro couldn’t advance as Edouard Julien hit a fly ball to short left for the second out. Alex Kirilloff then tied the game by lashing a double down the left-field line.

In the 10th, Tim Anderson’s two-out double off Jhoan Duran scored the automatic runner to put Chicago back on top, 4-3. But in the bottom half of the inning, Gallo made his big contribution to the win. He entered the game to pinch-run for Donovan Solano as the Twins’ automatic runner. Gallo moved to third on a wild pitch, then tagged up when Kyle Farmer hit a high pop fly behind first base.

Right fielder Oscar Colás had a long run for the ball, and he stumbled as he made the catch. As he fell to the ground, Gallo took off for home and easily beat the throw, tying the game at 4.

“I was going to just deke him and make him throw home because if he overthrows it or whatever,” Gallo said. “I saw him awkwardly catch it, go to the ground, and my instincts took over. I put my head down and ran. I was going home, and I was like, ‘Well, hopefully this pays off, because if this doesn’t, I’m going to look like an idiot.’ I wasn’t really sure how he really fell. I just saw him catch it awkwardly, my instincts took over, and I just went.”

After Griffin Jax and Emilio Pagán each pitched a scoreless inning, the Twins loaded the bases with nobody out in the 12th. The White Sox got outs at home and first when Christian Vázquez hit into a double play, but Jeffers followed with a line drive to right-center for the walk-off win.

It was Jeffers’ third hit of the game, bumping his batting average up to .272. He’s quickly becoming one of the players the Twins want to see at the plate in big moments.

“He’s made some nice adjustments at the plate this year,” Baldelli said. “Today was just another example of it -- getting a good pitch, just driving the ball the other way hard like that. I mean, that’s good hitting.”

It kicked off a raucous celebration, though two of Jeffers’ teammates did their best not to get too close to the crowd.

“I lingered in the back a little bit,” Gallo said. “Going through the line, not really touching, just elbows.”