The Pirates, winners in 10 of their last 12, have a five-game lead over Milwaukee with six games remaining for both teams. Any combination of two Pittsburgh wins or Brewers losses will guarantee the Pirates at least a spot in the NL wild-card game for the second straight year.
The Pirates still have hopes of winning the NL Central, but they began the night 2 1/2 games behind first-place St. Louis.
McCutchen, the 2013 NL MVP, hit his 24th homer in the sixth off starter Aaron Harang.
Pittsburgh has played three consecutive 1-0 games, winning the past two.
Liriano (7-10) allowed three hits, walked four and struck out seven in six innings. He extended his consecutive scoreless streak to 28 innings.
Liriano has a 0.69 ERA over his last five starts and 39 innings. He left the game when Jose Tabata pinch-hit in the seventh.
Mark Melancon faced four batters in the ninth to earn his 32nd save in 36 chances.
Atlanta lost its fourth straight to drop to 4-15 in September, worst in the majors. The Braves were eliminated from playoff contention Sunday.
The team's struggles, combined with a bloated payroll and punchless offense, led to the firing of general manager Frank Wren earlier in the day.
Harang (11-12) allowed four hits and one run with two walks and seven strikeouts in seven innings.
Atlanta, dragged down again by a sluggish offense, fell to 8-53 when scoring two runs or less.
Pirates: RHP Gerrit Cole (10-5) has won three straight starts and seven of his last nine decisions.
Braves: LHP Alex Wood (11-10) helped beat the Pirates in his only start against them on Aug. 19, but did not receive a decision.
Pittsburgh's starters have a streak of 23 consecutive scoreless innings. ... Jared Hughes pitched the seventh and John Holdzkom the eighth to help the Pirates' bullpen lower its ERA to 1.15 over its last 17 games.