Robinson Cano also drove in a run for the Yankees, who rose above .500 for the first time this season with their fourth win five games.
New York's Johnny Damon had three hits, while Rodriguez and Cabrera both had two hits.
Winner Mike Mussina (10-4) gave up three earned runs and six hits in six innings to get his ninth win in his last 10 decisions.
Houston's Carlos Lee blasted a three-run homer into the left field seats in the bottom of the first.
The losing pitcher was starter Wandy Rodriguez (2-3).
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes