Thomas Robinson scored 15 points and Greg Smith grabbed a career-high 13 rebounds off the bench for the Rockets. Asik also grabbed 11 rebounds for Houston, which has won four of five games on its current homestand.
The outcome was decided after three quarters, and Houston's starters sat out the fourth, turning their attention toward Sunday's game with San Antonio.
"That was a big win for us, and now we've got an even bigger one coming up Sunday," Parsons said.
Shaun Livingston scored 14 points for the Cavaliers, who've dropped five in a row and nine of their last 11 games. Cleveland failed to reach 20 points in each of the last three quarters and shot 36 percent (31 of 86) for the game. Houston also had a 54-32 edge in rebounds.
"As I told our guys, it was the first game in a long time that I saw us being very disconnected on both ends of the floor," Cleveland coach Byron Scott said.
The Rockets currently hold the No. 7 spot in the Western Conference. After the Spurs come to town, Houston faces Indiana, Memphis and the Los Angeles Clippers next week.
"We could see some of these teams coming up (in the playoffs), like Memphis and the Clippers," Parsons said. "It's a big test for us, to see where we stand with the elite teams."
The injury-depleted Cavaliers are hardly one of those, and the Rockets started to take control in the second quarter.
Harden returned after a long rest with 6:44 remaining in the first half, promptly stole the ball from Wayne Ellington and raced for a one-handed dunk. The Rockets ranked sixth in steals (8.51 per game) coming into Friday. Harden and Carlos Delfino sank back-to-back 3-pointers later in the quarter as the Rockets stretched the lead into double digits.
Livingston and Ellington sank jumpers in the final two minutes as the Cavaliers briefly seemed to find their shooting touch. But Delfino just beat the halftime buzzer with his second 3-pointer and Houston led 58-43 at the break.
Houston outrebounded Cleveland 14-5 in the second quarter and held the Cavaliers to 7-for-18 shooting.
"The entire defensive mindset was amazing," Harden said. "It was probably one of our best performances we've had on the defensive end all year."
Cleveland's shooting was even worse in the third quarter and Houston blew it open.
The Rockets found little defensive resistance inside and Asik and Parsons cut inside for easy baskets early in the third quarter to extend the lead. The Rockets continued to control the boards, particularly Asik, who was fouled making his 10th rebound with 6:49 left in the third quarter. He split two free throws, then dunked 30 seconds later for a 69-51 lead.
Last month, Houston squandered 17-point leads in consecutive games and lost. Parsons knew that wasn't going to happen on Friday night.
"We've had tendencies of getting big leads and then letting them (opponents) come back in," he said. "I thought it was big to keep our foot on the gas pedal and not look back and not let them keep climbing and give them any hope."
Harden and backup point guard Patrick Beverley sank 3-pointers in the last two minutes of the quarter and Houston led 87-61 heading to the fourth. The Cavaliers went 6 for 24 from the field in the third quarter.
"We just seemed like we were on our heels, waiting to see what they were going to do," Scott said.
The Cavaliers blew a 27-point lead in a 98-95 loss to Miami on Wednesday night and they were once again missing their top three scorers. Point guard Kyrie Irving (23 points per game) may miss the rest of the season with a left shoulder sprain, center Anderson Varejao (14.1 ppg) is definitely out for the year with a torn quadriceps and rookie guard Dion Waiters (14.7 ppg) is out indefinitely with a sore left knee. Scott said before the game that Waiters will be re-evaluated next week.
The Cavaliers have lost six in a row in Houston. ... Cleveland failed to reach 100 points for the ninth time in 11 games. ... Harden reached 20 points for the 57th time this season. ... Asik recorded his 29th double-double of the season and his first since March 6. ... Lin scored four points for Houston, snapping a streak of three consecutive games with at least 20.
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HOUSTON, TX - MARCH 22: Greg Smith #4 and Thomas Robinson #41 of the Houston Rockets reach for a rebound against...