Sims opened the scoring with a 5-yard run to cap the first drive of the game, then took a screen pass from David Piland 27 yards for another touchdown just before halftime. That put the Cougars (2-3) ahead 31-14.
Sims' previous career high was 207 yards rushing in last season's 73-17 victory over Tulane.
Piland, who was 31 of 41 for 321 yards, also connected with Dewayne Peace on a 16-yard score and added a rushing touchdown, as did Kenneth Farrow. Matt Hogan made all three of his field-goal attempts, including a 50-yarder, as Houston improved to 7-7 against the Mean Green (2-4).
Brandin Byrd led North Texas with 96 yards rushing, and Jeremy Brown, Antoinne Jimmerson and quarterback Derek Thompson ran for scores.