The Pelicans were in front by seven heading into the fourth period and New Orleans still led by seven when the clock ticked under 3 minutes.
Houston then closed the game on an 11-1 run, the only New Orleans point during that stretch coming when Anthony Davis made 1-of-2 from the foul line with 47 seconds to play.
That free throw tied the game at 100-100, but Harden then scored on a layup to give the Rockets the lead for good and a foul shot by Chandler Parsons with 11 seconds to play accounted for the final score.
Darius Miller missed a 3-point attempt that would have tied the game with three seconds left.
Houston won its third in a row, getting 26 points and seven assists from Harden along with 25 points from Terrence Jones.
Eric Gordon scored a season-best 35 points for the Pelicans, who have lost seven straight.
The teams were called for a combined 62 fouls, leading to 70 free throws -- 41 of them by the Rockets.