The French star was ejected for elbowing Naz Reid in the jaw early in the second quarter.
Timberwolves star Anthony Edwards scored 16 of his 36 points in a frantic fourth quarter that featured five lead changes.
Rudy Gobert converted a three-point play that put the Timberwolves up for good, 103-101, with 3:02 remaining, and Ayo Dosunmu converted another three-point play to push Minnesota's lead to 110-103 as they closed out the win in a game in which neither team led by more than nine points.
Defensive Player of the Year Wembanyama was tossed from a game for the first time in his NBA career early in the second quarter.
Bottled up by Reid and Jaden McDaniels after an offensive rebound, he turned back toward Reid and jabbed his elbow, sending the Timberwolves player sprawling.
But with 24 points apiece from De'Aaron Fox and Dylan Harper and 20 from Stephon Castle, the Spurs kept themselves in it and led 94-86 with 8:51 to play.
"When Wemby got thrown out of the game, we came out thinking it was going to be easy," Edwards said.
"But those guys are really good even without Wemby. So we just had to play hard, and I had to just take it upon myself to try to get us a win."
Reid finished with 15 points and nine rebounds, and McDaniels added 14 points for the Timberwolves, who assured the series will return to Minneapolis for game six after the Spurs host game five on Tuesday.