Dalembert's winning basket climaxed a wild game in which the Rockets lost a big lead in the fourth quarter and rallied from a deficit early in the extra period.
Houston won its fifth straight and moved a game above .500 after opening the season 3-7. The Hornets have lost six in a row.
The Rockets outscored New Orleans in each of the first three periods, and then managed only seven points in the fourth period while the Hornets were making a charge. Houston did not score during the final 2 minutes of regulation and Jarrett Jack produced the last point for New Orleans at the foul line with 18 seconds left.
New Orleans built a five-point lead in overtime but the Rockets rallied into a tie when Luis Scola hit two free throws with 1:10 remaining. Dalembert provided the winning points after rebounding a missed layup by Kevin Martin.
The Hornets' Marco Belinelli missed a fadeaway jumper as time expired.
Couple mistakenly served bag of cash at McDonald's drive-thru
Exploding whale video goes viral on Internet