The crowd at Houston's Toyota Center was chanting "One more three! One more three!" when Michael Carter-Williams drained the record-breaker from beyond the arc with 31.1 seconds remaining and victory assured.
Gary Clark's three-pointer with 2:42 to play had tied the previous mark of 25 set by the Cleveland Cavaliers against Atlanta in March 2017.
Reigning NBA Most Valuable Player James Harden had six three-pointers on the way to 35 points. Chris Paul added five from beyond the arc and Gerald Green and Eric Gordon made four apiece as the Rockets - who endured a rough start to the season - got back to their free-wheeling ways in a fifth straight victory.
"We're just playing better," Rockets coach Mike D'Antoni said. "When you have the right spirit, you're doing the right things, hustling, stuff falls in. If you don't, you don't make them.
"Our energy is right the last five games," D'Antoni added. "We've just got to keep it there."
Golden State Warriors coach Steve Kerr said energy was a problem for the two-time defending champions in a 108-103 loss to the Utah Jazz in Salt Lake City.
Stephen Curry scored 32 points, but the Warriors shot just 40 percent from the field and 32.3 percent from three-point range.
Kevin Durant finished with 30 points, but not before making just six of 18 from the field through the first three quarters and Klay Thompson scored just 12 points, connecting on just three of 12 shots and missing all four of his three-point efforts.
"It's not surprising, honestly," Kerr said. "We're not moving the ball, we're not playing the way we've played the last few years where the ball is really moving and we're generating great shots."
Kerr noted that the Jazz, whose shooting percentage was even worse than the Warriors' at 39.8, didn't have that great of a game themselves.
"We let them off the hook a little bit," Kerr said. "We made a lot of mistakes. We made it close with a few shots down the stretch, but we didn't really play our game."
Things were tight in Toronto, where Fred VanVleet drained the go-ahead three-pointer with 26.4 seconds left as the Raptors erased a 17-point second-half deficit to improve their NBA-leading record with a 99-96 victory over the Indiana Pacers.
Kawhi Leonard scored 28 points and Pascal Siakam added 17 for the Raptors, who had lost two straight but avoided a second three-game losing streak this season.
VanVleet scored nine of his 11 points in the final quarter as the Raptors again overcame the absence of point guard Kyle Lowry, who missed his third straight game with a left thigh injury.
"To be honest, I was really disappointed with how we were playing," Toronto coach Nick Nurse admitted. "In the end we finally started guarding. We told them to stay with it ... keep eating into them and hang in there and we might be able to pull it out."
The Phoenix Suns' surge continued with a 111-103 victory over the Celtics in Boston.
Devin Booker scored 25 points with eight assists a steal and two blocked shots for Phoenix. Rookie Deandre Ayton added 23 points and 18 rebounds for the Suns, who are last in the West but have now won four straight.
Making the defeat more painful for Boston, center Aron Baynes suffered a broken bone in his left hand in the first quarter and will be out indefinitely.
In Orlando, LaMarcus Aldridge scored 20 points to lead five San Antonio players in double figures in the Spurs' 129-90 victory over the Magic.
In Philadelphia, Ben Simmons' triple-double of 13 points, 10 assists and 11 rebounds helped the 76ers to a much-needed 131-109 victory over the New York Knicks.
Oklahoma City's Russell Westbrook also notched a triple-double, delivering 19 points, 17 assists and 11 rebounds in the Thunder's 132-113 victory over the Kings in Sacramento. Paul George led the Thunder with 43 points.