Khris Davis led off the top of the 11th with a double to left off Kevin Siegrist (0-1). Overbay followed with a single up the middle that deflected off of Mark Ellis' glove as Davis trotted home without a throw. Francisco Rodriguez earned his 13th save with a scoreless bottom of the 11th.
Tyler Thornburg (3-0) struck out four in two scoreless innings for Milwaukee, which has taken the first two games of this series and improved to 11-1 on the road this season.
Overbay finished 2-for-5 with two RBI, while starting pitcher Kyle Lohse fanned nine in six innings and helped himself at the dish with a two-run single. Lohse allowed three runs on six hits.
Yadier Molina homered for St. Louis, which has lost five of seven. Molina, Matt Adams and Johnny Peralta all had two hits in the setback.
St. Louis got to Lohse immediately, putting three across in the bottom of the first inning. Allen Craig drew a walk around Matt Carpenter's strikeout and Matt Holliday's lineout, but Adams doubled to put two on for Molina, who made Lohse pay for leaving a fastball up in the zone by taking it out to left- center.
The 3-0 margin held until the fourth, when Overbay's RBI single put the Brewers on the board. Lohse plated a pair inning later, tying the ball game with a two-run single.
Both teams scored a run in the seventh. Carlos Gomez's solo homer to left made it 4-3 in favor of the Brewers, but Craig's opposite field triple to right past a diving Elian Herrera plated Carpenter to tie the score.