Adrian Peterson rushed for 211 yards on 35 carries and set up the game-winning boot with an 11-yard run in the extra frame for Minnesota (2-8-1).
Walsh had kicked an apparent game-winning field goal earlier in the overtime, but it was nullified by a face mask penalty on Rhett Ellison -- he then missed a 57-yard try.
The Minnesota kicker had forced overtime with a score-tying, 30-yard boot with 24 seconds left in regulation.
Matt Cassel went 20-of-33 through the air for 243 yards, a touchdown and interception after replacing Christian Ponder in the first half. Ponder exited with a possible concussion after he was hit in the head by Chicago lineman Shea McClellin.
Josh McCown completed 23-of-36 passes for 355 yards with a pair of TD passes to Alshon Jeffery for the Bears (6-6), who missed a chance to pull even with NFC North-leading Detroit.
Jeffery racked up 249 receiving yards on 12 catches.