Reserves Marcus Morris and Toney Douglas both hit a pair of 3s early in the second quarter as the Rockets surged to a 47-38 lead. Houston started 7 for 10 from the field overall in the quarter. Morris stayed on the floor when the starters returned, and scored on consecutive drives to stretch the lead to 52-40.
Harden, the NBA's reigning Sixth Man of the Year, liked what he saw from the Houston bench.
"They lifted us up," Harden said. "Toney and Carlos (Delfino) and Marcus Morris really did a good job, coming in and bringing that energy."
New Orleans defended the perimeter better in the third quarter and trimmed the deficit to six. Vasquez, fourth in the NBA in assists coming into the game, twisted his left ankle on a drive late in the third quarter. He came out of the game and limped to the locker room.
Houston led 85-76 after three, then gave away four turnovers in the first 4 minutes of the final quarter. Vasquez returned and guarded Harden, who swished a jumper from the top of the key for a 95-88 lead with just over 4 minutes to go.
The 6-foot-9 Al-Farouq Aminu switched to guard Harden after that, and Harden passed to Parsons for a 3-pointer with 3:27 remaining.
Vasquez then sank a pair of 3s to fuel a quick 8-0 Hornets run that cut the gap to 98-96 with less than 2 minutes to play. Parsons just beat the shot clock with an awkward fadeaway jumper to put Houston up by four.
Aminu and Vasquez missed 3-pointers in the final 5 seconds, and Houston held on.
Notes: Houston coach Kevin McHale missed his third straight game since taking an indefinite leave to address a family matter in Minnesota. Assistant coach Kelvin Sampson said the team still has no timetable for McHale's return. ... Former Rockets center Ralph Sampson was honored at midcourt during a timeout in the second quarter. Sampson, the top overall pick in the 1983 draft who guided Houston to the 1986 NBA Finals, was inducted into the Naismith Hall of Fame in September. ... The Rockets' 39 second-quarter points and 64 first-half points were season highs.