Rogers amassed 338 yards, completing 24-of-37 passes as Green Bay (3-3) got back on the winning tracking following a loss to Indianapolis last week.
Three of his scoring strikes went to Jordy Nelson, who finished with nine passes for 121 yards. Randall Cobb made seven grabs for 102 yards in the win.
Rogers also found James Jones for two scores.
The Texans (5-1) were led by Matt Schaub, who found the mark on 20 of his 33 passes for 232 yards, but was intercepted twice as Houston fell from the ranks of the undefeated.
With Houston's loss, Atlanta (6-0) remained as the NFL's only unbeaten team.