The only other Brewers pitcher to accomplish the feat was Manny Parra on June 6, 2010, in St. Louis.
After fanning Devin Mesoraco and Edinson Volquez, Gallardo made Brandon Phillips his 10th strikeout victim of the night, but the Reds second baseman reached first when the ball skipped away from catcher Jonathan Lucroy for a wild pitch.
"It was a tough pitch for Lucroy to block," Gallardo said. "I was trying to keep it down and not leave it up in the zone. Being able to command my breaking stuff has made my fastball that much better."
Gallardo then struck out Edgar Renteria to end the inning. It was Gallardo's 11th strikeout on the night, and the righty finished with 13 in six innings.
The last time four Reds batters fanned in one inning was April 26, 2006, against Jon Rauch in Washington.
"It was impressive," Ryan Braun said. "It's great that he's finishing the season strong for us. He's throwing the ball better than he has all year. It's great timing for us. Hopefully, he'll pitch in a lot of big games for us down the stretch."
Jeff Wallner is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.