Budinger scored 18 points while subbing for the injured Brandon Roy, who left at halftime with a sore right knee. The three-time All-Star is attempting a comeback after chronic knee issues forced him to retire from Portland before last season.
Kevin Love (broken hand), Ricky Rubio (torn ACL) and J.J. Barea (sprained foot) were already out for Minnesota, but that just doesn't seem to matter right now.
"It's OK," Kirilenko said with a shrug. "We'll still keep winning. Injuries, that don't matter. Winning is what matters.
Alexey Shved had 11 points and seven assists and Nikola Pekovic added 13 points and eight rebounds for the Timberwolves (4-1), who are three games over .500 for the first time since they were 20-17 in the 2006-07 season.
George Hill had 29 points, seven assists and five rebounds for the Pacers, who have lost three in a row. David West had 19 points and 13 boards.
"We just have to learn how to finish the game," Hill said. "We're there at the end of the game and that's the good part. There's no use in hanging our head now, there's 75 games left in the season, but we have to learn how to finish it."
Shved, a rookie from Russia, ran the pick-and-roll like a seasoned veteran against Indiana's stout defense, creating scoring chances for himself and his teammates.
His layup gave the Wolves a 78-69 lead with eight minutes to go in the game. But he also picked up his first American technical foul during a 7-0 run by the Pacers that got them within two points. West's putback two minutes later tied it at 86.
Shved followed with a tough drive and another layup off a steal from Kirilenko, and the Wolves used an 8-2 spurt to open a 94-88 lead with under a minute to play.
But Hill converted a three-point play, then made a tying 3-pointer from the top of the arc with 3.8 seconds remaining.
The final play was recommended by assistant coach Bill Bayno and designed for Kirilenko, who grabbed the inbounds pass on the right wing, calmly took a few dribbles and looked toward the basket. Budinger was out past the 3-point line and started cutting to get into position for a possible tip-in of a missed shot.
But Pacers guard Gerald Green wasn't paying attention, and Budinger wound up wide open under the basket. Kirilenko found him for the game winner, sending the Target Center crowd into a euphoric roar.
"I lost vision of my own man, a careless mistake," Green said. "I don't know what to say. I get paid too much to make that kind of mistake."
Roy sat out all of last season, but felt rejuvenated this summer after receiving an experimental treatment to try to address the lack of cartilage in both knees. In need of a veteran shooting guard who could get his own shot late in games, the Wolves signed him to a two-year deal. He played at least 21 minutes in each of the first four games this season, issuing no complaints.
Coach Rick Adelman said it was too soon to tell how serious the injury was, but Roy planned to make the trip to Chicago for the team's game on Saturday in case he was feeling good enough to play.
The Pacers have some serious injury problems of their own. They found out this week they are going to have to play without leading scorer Danny Granger for the next three months because of an issue with his left knee, dealing a big blow to a scrappy team that gave the Miami Heat all they could handle in the playoffs last season. They've struggled to replace his offense, only topping 90 points twice this season.
"Our margin for error is very small," Pacers coach Frank Vogel said. "We've got young and inexperienced players in there at crunch time. We dropped a couple of games because of it. That's what we're trying to overcome without Danny Granger."
Pacers C Roy Hibbert had 10 points, but was on the bench most of the fourth with foul trouble. ... The Pacers are 0-3 on their current road trip. ... Barea will not make the trip to Chicago. He will be evaluated again on Sunday, with the possibility of joining the team in Dallas.