HOUSTON — The Houston Rockets were down three starters Friday night, but still came away with a big win.

James Harden had 33 points and eight assists as the short-handed Rockets clinched a playoff spot with a 120-110 victory over the Minnesota Timberwolves.

Harden shot 9 for 19 from the floor, including 6 for 12 on 3-pointers. Josh Smith added 16 points, nine rebounds and 11 assists and Trevor Ariza scored 14 points for the Rockets, who shot 53 percent, including 20 of 44 on 3s and dished out 34 assists.

“That’s what we’ve been doing these past few weeks, just moving the basketball,” Harden said. “Making sure everyone touches the basketball. Making sure we get good shots.”

The Rockets were without starters Terrence Jones, Patrick Beverley and Donatas Motiejunas, who missed the game due to injuries.

Dwight Howard had 18 points on 8-for-9 shooting in 21 minutes in his second game back from a right knee injury. With Houston playing a back-to-back Sunday and Monday, Houston coach Kevin McHale said he would not play in both games.

“We try to keep him around 20 minutes instead of 15 or 16,” McHale said. “We’ll see how he responds and we’ll go again from there.”

Jason Terry scored 17 points and Corey Brewer had 11 points and 10 rebounds for the Rockets, who are in third place in the Western Conference and clinched a playoff spot for the third straight year.

“We’re a team on a mission,” Smith said. “We’re a team that doesn’t make excuses. We want to be able to come in each and every game and be mentally prepared for the postseason no matter who we play.”

Andrew Wiggins led the Timberwolves with 31 points on nine of 17 shooting, and he hit 12 of 15 from the free throw line.

“He’s playing at a really, really high level,” Minnesota coach Flip Saunders said of Wiggins. “He’s doing things that I really didn’t envision he’d get to as far advanced as he has gotten to at this point. It seems like every time we give him more responsibility, he continues to thrive.”

Chase Budinger added 23, Gorgui Dieng had 18 points and 12 rebounds, and Adreian Payne scored 14 points.

Minnesota, which was also short-handed while using only eight players, shot 49 percent from the field — including 6 for 14 on 3s. The Timberwolves, which have lost three of their last four, were outrebounded 41-31.

“Against a good team, when we make mistakes, they are going to make you pay,” Wiggins said. “That’s what makes them a great team. They had a lot of good shots. They hit 20-something 3s, and they all seemed like good shots.”

Houston started the fourth by outscoring Minnesota 9-4 to open up a 99-84 lead on Pablo Prigioni’s 3 less than 3 1/2 minutes into the quarter. However, the Timberwolves answered with a 10-2 run to cut the lead to seven on Wiggins’ two free throws with 6:24 left.

After the Rockets pushed the lead back to double digits, Dieng closed the lead to seven one final time with a three-point play. Houston responded with on a 9-2 run, capped by Howard’s dunk with 2:49 remaining to give the Rockets a 115-101 lead.

Houston led 60-50 at halftime behind 15 points from Harden and 12 from Smith.