Cueto (5-2) pitched well in his first appearance since June 28, when he went on the shelf with a back injury. The right-hander scattered five hits, issued one walk and struck out five.
Cozart opened the scoring with a two-run homer in the second inning and added a two-run single in the fourth for third-place Cincinnati, which came into the contest trailing National League Central co-leaders Pittsburgh and St. Louis by 3 1/2 games.
The Reds increased their NL wild-card lead over idle Washington to five games with the win.
Astros starter Erik Bedard (4-11) yielded four runs on four hits over four full innings.
Matt Dominguez got the only RBI for Houston, which fell in the first of a three-game interleague series.
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