The Brewers barely survived a St. Louis rally in the bottom of the ninth as the Cardinals put three men aboard with two outs in a 4-4 tie game. John Axford (1-3), however, struck out pinch-hitter David Descalso to end the threat.
Then in the 10th, Milwaukee loaded the bases with two outs against Joe Kelly (0-2) and Bianchi, who had only five previous at-bats in seven games since being activated from the disabled list, sent a single up the middle for two runs.
Jim Henderson racked up his eighth save for the Brewers, who evened their three-game series.
Jean Segura and Ryan Braun each contributed three hits and two RBI in the win.
Matt Carpenter drove in two runs while Jon Jay and Pete Kozma each added an RBI for National League Central-leading St. Louis.