Brendan Donovan scored from first on Nolan Arenado's single when Elly De La Cruz booted the ball in short left field for his major-league leading seventh error, making the score 2-1.
Neither team's starter returned following the rain delay.
Liberatore (2-3) allowed two runs and two hits in three innings for the Cardinals. Reds left-hander Andrew Abbott gave up a run on four hits over four innings.
Steer hit a solo homer, his third of the season, off Riley O'Brien to make the score 5-1 in the sixth.
Santiago Espinal's two-run single in the seventh pushed the Reds' lead to 8-1. He went 2-for-4 with two RBIs.
Reds reliever Graham Ashcraft (2-2) retired nine straight with four Ks to earn the victory and extend his scoreless streak to five innings.
Key moment
Matt Svanson replaced Liberatore in the fourth following the rain delay and allowed two singles and a walk to the first three batters to load the bases. The Reds scored twice in the inning to grab a three-run lead.
Key stat
Trevino hit eight homers in 73 games last season for the Yankees. He has homered three times in 25 games so far this season.
Up next
Cardinals: RHP Sonny Gray (3-0, 3.60) will start Friday's series opener against the Mets.
Reds: RHP Hunter Greene (3-0, 2.70) will start Friday's series opener against the Nationals.
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