Dwight Howard had 24 points and 18 rebounds, and Harden scored 11 of his 21 points in the fourth quarter in the Rockets' 107-98 comeback victory.
"It was winning time," Harden said. "I was struggling the first three quarters and couldn't find the rhythm when my teammates needed me the most. We got the ball moving and Jeremy made a couple of good threes. Chandler (Parsons) had a good put back and then Dwight got an and-one. Everybody picked up the intensity a little bit."
It was the second straight game Houston rallied in the fourth for a win and marked the first time since December 2009 that the Rockets have won three straight games within the division. Houston beat San Antonio on Christmas and topped Memphis on Thursday night.
"We didn't shoot it well," Houston coach Kevin McHale said. "I know at one time I looked up, I thought we were two for 19 from the three-point line. It felt like they made every three. They were 10 for 22. ... We found a way to win, but it was another in a long line of games that feel like you are pulling teeth."
Howard was 10 of 12 from the floor, helping to keep Houston in the game through the first three quarters with 20 points in that span.
"I just tried to play out of the double team," Howard said. "When they doubled, I tried to make the good play, and when they didn't double, I tried to make the better play for myself."
Parsons added 19 points and seven rebounds, and Terrence Jones had 17 points and eight rebounds to help Houston win its third straight game and snap New Orleans' winning streak at two.
Lin had all 10 of his points in the fourth quarter after scoring 14 of his 18 points in the fourth against Memphis. The Rockets made three of five 3-point attempts in the fourth quarter after going 3 of 21 from long range in the first three quarters.
"It's definitely not the ideal plan or ideal strategy," Lin said. "I'm thankful Coach McHale let me keep going. I was able to finally get a little bit of a rhythm in the last two games. I have to do a much, much better job and be more aggressive in the first three quarters."
Houston was 25 of 32 from the free-throw line, while New Orleans was 6 of 8.
"Anything I say is going to get me in trouble," New Orleans coach Monty Williams said about the free-throw difference. "OK, so let's just leave it at that. Thirty-two to eight."
"I think we really didn't execute down the stretch," Evans said. "It was a tough loss. I think we played hard and fought, but in the fourth quarter, our execution wasn't that good. They hit some big shots. ... They were shooting it from far out, and it kind of tough, but they made their shots, and we can't do anything about that."
After New Orleans opened a 92-88 lead with 4:54 left on Davis' alley-oop dunk, Jones started Houston on a game-ending 19-6 run with a three-point play.
Following Davis' jumper, Lin tied it at 94 with a 3-pointer with 3 minutes remaining. Then, Harden put the Rockets ahead for good with a 3-pointer to give with 3:14 remaining.
"We were in it the whole game, and we were giving ourselves a chance to win the game," Davis said. "We tried to send a couple of guys at Dwight and give him different looks. He found Jeremy Lin in the corner for a three and then James came down and hit a three. They just made big shots, and we didn't execute at the end. We have to come out and know what we're running and execute."