Kevin Love had 17 points and 12 rebounds and Minnesota took advantage of Wade's absence for just their fifth road win of the season, 91-88, over the Miami Heat on Tuesday night.
Flynn added 16 points and three steals for the Timberwolves, who snapped a six-game losing streak. They had won just once in their previous 13 games away from Target Center.
"Any win is good, of course, but this was especially satisfying," Timberwolves point guard Jonny Flynn said.
And this home loss to the second-worst team in the league could come back to haunt the Heat, who are clinging to a playoff spot.
Dorell Wright scored a career-high 26 points off the bench and Jermaine O'Neal added 18 for Miami, which came out sputtering against the lowly Timberwolves (14-44), who have the worst record in the Western Conference.
"With what we have at stake, and that's not any disrespect to Minnesota, it's a shame and I could not be more disappointed with that effort or focus to come into tonight," said coach Erik Spoelstra, whose Heat currently are in seventh place in the East. "Give Minnesota credit for coming in here and kicking our tails all over the place. They deserved that."
The Heat played its third straight game without Wade, the All-Star MVP, and starting point guard Rafer Alston. Wade is listed as day to day with a strained left calf, while Alston is dealing with a bruised right hand.
They were sorely missed.
The Heat got off to a slow start without Wade, shooting 6-of-18 for a season-low 15 points in the first quarter to go down by nine.
They trailed almost the entire game except for a small stretch early in the third quarter, and couldn't string together a solid run to overtake Minnesota.
"We can't just start off lackadaisical and get down by 17 points in the first half and expect to just climb back when we decide to play," said Heat forward Michael Beasley, who finished with 14 points and nine rebounds. "Collectively as a team, there was no energy, no passion. We just didn't come tonight."
Wright got the Heat close, scoring 11 points, including three 3-pointers, to help overcome a 14-point deficit.
Wright hit a 3-pointer, Quentin Richardson connected on all three of his free throws, and Daequan Cook had a jumper from the left side to make it 87-84.
Beasley's tip-in, and Wright's jumper after a lay-up by Flynn made it a one-point game with less than 30 seconds left on the clock.
But Wolves rookie Wayne Ellington knocked down both of his free throws, and Cook missed a 3-pointer as time expired to give Minnesota its first victory in Miami since the Kevin Garnett era in 2003.
"We did enough good things tonight to get a win," said Minnesota coach Kurt Rambis. "This is a microcosm of how we've been all year. We play well in pockets."
It was good enough to beat the Heat (29-29), who is currently seventh in the Eastern Conference standings, just ahead of Charlotte and Milwaukee, which are both 27-28.
"They came in like they had more urgency or desperation to their season and it's really disgraceful that it came down to that," said Spoelstra.
Heat coach Erik Spoelstra said he splashed some Jackson 5 footage into game film to inspire his players. It was in response to comments made by TNT analyst Charles Barkley last year referring to Wade's teammates as a bunch of Tito Jacksons. "Ultimately an 82-game season is long. So sometimes there are different ways to inspire players," Spoelstra said. Minnesota F Ryan Gomes hit a 3-pointer in the first quarter after going 0-for-9 from deep in his last four games. O'Neal's tip-in in the second quarter put him over the 12,000-point mark for his career.