It was an 84-84 game with 6:24 left when Asik hit a reverse layup while being fouled. He converted the free throw and Houston put together a 17-4 run that blew open the contest.
James Harden scored 31 points for the Rockets and handed out seven assists in what was Houston's second straight win.
Asik contributed 21 points and eight rebounds while Patrick Patterson had 15 and 10 boards.
New Orleans has lost 14 out of 16 games and has not defeated a division opponent in five tries this season.
The Hornets were led by Ryan Anderson with 18 points and seven rebounds.