It will be Houston’s second trip to the conference finals in four years and the first ever for Paul, The Associated Press reported.
The point guard has been criticized for failing to get past the second round in his nine previous trips to the postseason.
Houston will meet Golden State after the Warriors finished off the New Orleans Pelicans on Tuesday.
Utah’s star rookie Donovan Mitchell shot nine of 17 from the field and had 24 points for Utah before leaving with about seven minutes left with an apparent left leg injury.
Mitchell was injured when James Harden stole the ball from him and capped an 11-5 Rockets’ run with a dunk that gave Houston a 92-87 lead.
Mitchell grabbed his left leg on the play. He had to be helped to the bench and was quickly taken to the locker room with the help of two people.
Paul, a nine-time All-Star in his first season with Houston after an off-season trade from the Los Angeles Clippers, also had 10 assists and seven rebounds.
Houston made 18 three-pointers in the game to give the team 10 or more three-pointers in a playoff-record 16 straight games.
P. J. Tucker scored a playoff career-best 19 points, and Harden added 18 points for the Rockets.
Warriors 113 Pelicans 104
Stephen Curry, in just his fourth game back from injury, led the Warriors with 28 points in Golden State’s win over New Orleans, which secured the Warriors their fourth consecutive appearance in the Western Conference finals.
Kevin Durant had 24 points, Klay Thompson had 23 and Draymond Green just missed a triple-double with 19 points, 14 rebounds and 9 assists.
The Warriors raced to a huge lead in the third quarter, but had to survive an 18-2 run by the Pelicans in the fourth quarter.
Anthony Davis finished with 34 points for New Orleans.
Winners of two of the last three NBA titles, the Warriors will have their hands full with the Rockets, who broke Golden State’s run of three straight years as the No. 1 seed in the Western Conference.