Carlos Martinez retired the first 12 batters he faced, but allowed a single in the fifth inning.
So far, it has been the Brewers' only hit of the evening. First baseman Travis Shaw was the culprit, lining the single to center field and then advancing to second on a wild pitch.
Martinez has struck out two batters against two walks, and has thrown just 57 pitches.
On offense, the Cardinals are also without a run. Their best opportunity to score came in the bottom of the fifth when they got two men on for the first time, but shorstop Aledmys Diaz grounded out to end the inning.