It was Barnes' rebounding that excited Warriors coach Mark Jackson the most.
Barnes had 10 points and 11 rebounds, Klay Thompson scored a season-high 24 points and Golden State beat Minnesota 96-85 on Saturday night.
The seventh overall pick in this year's draft, Barnes had three points as part of a 19-2 run in the fourth quarter, but it was his emphatic dunk over Pekovic that had the Oracle Arena crowd buzzing.
After Alexey Shved's layup gave the Timberwolves a 41-38 lead, Barnes raced down the court and took a bounce pass from David Lee before grabbing the ball with his right hand and slamming it through the hoop as Pekovic tried to stop him.
"Top, by far," Barnes said when asked where the dunk ranked in his basketball career. "It probably would have been a little bit better if it would have been and-one. I just wanted to finish strong."
Jackson called it a big-time play by his young rookie.
"Well it's behind Tom Chambers' (dunk) over me," Jackson said. "Harrison really showed his athletic ability and that's going to be one that he will remember for a long time to come. More importantly for him, he led us in rebounds. You've got to be committed as a big man to box out Pekovic and also Kevin Love."
Love, playing in his third game since returning from a broken right hand, had 15 points and 15 rebounds but couldn't prevent Minnesota from losing its fifth straight.
He wore a black protective pad on his hand most of the night before ripping it off and tossing it to the bench with six minutes remaining.
"It's very restricting," Love said. "I can't bend my hand all the way back and I couldn't get a good feel for the basketball. The doctor said it was OK to play but at the same time he warned that I'm coming back two weeks early and I have to keep working on my conditioning, my range of motion and shooting."
Stephen Curry had 20 points and six assists, while Lee added 17 points and eight rebounds for Golden State, which has won 10 of 12 against Minnesota.
The Warriors trailed most of the game but went on a 19-2 run, with reserves Carl Landry, Draymond Green and Barnes providing the bulk of the scoring. Landry had five points and Green had four to help Golden State go ahead for good.
Thompson was criticized earlier in the week after a poor shooting performance against Dallas on Nov. 19, but has been steady since. He shot just 1 of 8 from 3-point range but was 7 of 9 inside the arc and is averaging 21 points over his past three games. Landry finished with 18 points and nine rebounds off the bench.
Minnesota, still missing several key injured players, couldn't keep up and lost its fifth straight.
The Timberwolves made several mistakes along the way, blowing a 3-on-1 fast break in the first half, then shooting just 32.4 percent in the second half.
Not even a gift basket by Golden State's Andris Biedrins was enough to help coach Rick Adelman's struggling squad. Biedrins was battling a teammate for a rebound underneath Minnesota's basket when he accidentally tipped the ball into the hoop.
The Warriors also outrebounded the Timberwolves 48-39.
"A lot of it is the big men have to play better defense, and that's mostly me," Love said. "I have to take the blame, and some of the other bigs do, too, because we have to help each other out."
The Warriors have their own injury issues.
They lost key reserve Brandon Rush to a season-ending knee injury in their home opener on Nov. 2, and have been without center Andrew Bogut for nine straight games and backup forward Richard Jefferson for four.
Bogut, the No. 1 overall pick in 2005 who broke his ankle on Jan. 25, has played in only four games this season but the team said last week it hopes the 7-foot Australian can resume practicing Monday.
Love had six quick rebounds in his third game since returning from a broken right hand but was on the bench when the Timberwolves built a 35-24 lead with mostly reserves on the floor.
The Warriors came back and tied the score at 47-all on Thompson's short runner, but Jose Barea made a 9-foot jumper and Andrei Kirilenko followed with a dunk to give Minnesota a 51-47 halftime lead.