Harden hit a step-back jumper over Paul Zipser with 36.1 seconds remaining in the extra period and was fouled. He made the free throw to give the Rockets a two-point lead they never relinquished.
After losing to Atlanta on Thursday night, the Rockets improved to 12-1 this season in the second of back-to-back games.
The Bulls played without star forward Jimmy Butler, who was nursing a bruised heel. Starting in his place, Michael Carter-Williams had 23 points, nine rebounds and six assists before fouling out with two minutes remaining in overtime.
Harden hit a step-back jumper over Carter-Williams to tie the game at 108 with 27.3 seconds remaining in regulation.
On the next possession, Dwyane Wade lost his dribble when guarded by Trevor Ariza, leading to a shot-clock violation with 3.3 seconds to go. Harden tried the same move against Carter-Williams at the buzzer, but his shot fell short.
Chicago dominated the Rockets' interior defense, outscoring Houston 60-46 in the paint. Taj Gibson scored 20 points for the Bulls, and Wade had 19 points, nine rebounds and six assists.
The Rockets built a lead that reached 17 midway through the second quarter as they opened the period on a 26-7 run, all with Harden on the bench. Chicago cut Houston's lead to 60-49 at halftime.
The Bulls started the third quarter on a run of their own, outscoring the Rockets 24-12 out of the extended halftime break and entered the fourth quarter with a two-point lead.
In a special halftime ceremony, the Rockets retired Yao Ming's No. 11 jersey with a dedication that featured Yao's family, former teammates, fellow Hall of Famers Hakeem Olajuwon and Dikembe Mutombo as well as NBA Commissioner Adam Silver.
Westbrook also had 13 rebounds and 12 assists for his 25th triple-double this season and the 62nd of his career.
at Detroit 116, Minnesota 108: Marcus Morris scored a career-high 36 points for the Pistons, who overcame 5-for-20 shooting from its starting backcourt of Reggie Jackson and Kentavious Caldwell-Pope. Jon Leuer added a career-high 24 points for Detroit.
at Orlando 102, Toronto 94: Serge Ibaka scored 20 points and grabbed 12 rebounds while Evan Fournier added 20 points and 10 rebounds for the Magic.
Phoenix 105, at Sacramento 103: Devin Booker scored 33 points and made the game-winning jumper at the buzzer as the Suns snapped a five-game losing streak.
at Celtics 113, Lakers 107