Despite walking three batters, Wolf delivered his best outing of the season with six scoreless innings. But that was seven frames before the end of the game.
After a wild seventh, eighth and ninth innings, Parra and Chulk came on to toss four scoreless innings in the 10th through 13th. Chulk picked up the win, his first since Aug. 19, 2007.
"It was awesome," Chulk said. "It's one of those games that could start something really nice here."
Chulk tossed two innings, allowing just two hits and one intentional walk along with two strikeouts. He is 1-0 with a 6.75 ERA in three appearances with the Brewers since being called up from Triple-A Nashville on April 29.
Parra went two innings, allowing a hit and two walks with three strikeouts. He has not allowed a run in his last seven appearances, spanning 7 2/3 innings. Opponents have hit .087 (2-for-23) over that stretch.
"I was very impressed with Manny and Vinnie," said catcher Jonathan Lucroy, who caught the last six innings of the ballgame. "They came out and did their job, and executed very well. And I was very happy to see that. They battled their butts off, man, and that's all you can ask for."