The home side's quarterback turned the ball over three times in the fourth quarter and overtime, with the Wyoming product mishandling from a snap and fumbling in the end zone late in the game.
Kirk Cousins threw for 357 yards for the visitors, who moved to 8-1 and way out in front in the NFC North.
Minnesota's divisional rivals the Green Bay Packers produced their own overtime victory, as they snapped a five-game losing streak with a 31-28 result over the Dallas Cowboys.
Green Bay quarterback Aaron Rodgers seemed to shake off some of his troubles as he threw a trio of touchdown passes to rookie wide receiver Christian Watson.
The veteran also led a 55-yard drive that ended with Mason Crosby hitting a game-winning field goal to break the heart of former Packers coach Mike McCarthy, now with the Cowboys.
In earlier games, Tom Brady's Tampa Bay Buccaneers claimed a 21-16 win over the Seattle Seahawks, the Chicago Bears - despite a 147-yard rushing effort from their quarterback Justin Fields - were pipped 31-30 by local rivals the Detroit Lions and the Miami Dolphins blew away the Cleveland Browns 39-17.
The Tennessee Titans won 17-10 against the Denver Broncos, the New York Giants closed out the Houston Texans 24-16 and the Kansas City Chiefs were 27-17 victors over the Jacksonville Jaguars.
Linebacker TJ Watt's return from injury appeared to spark his Pittsburgh Steelers to a 20-10 win over the New Orleans Saints, while the Las Vegas Raiders squandered a fourth-quarter lead to fall 25-20 to the Indianapolis Colts.
The Arizona Cardinals won 27-17 against reigning Super Bowl champions the Los Angeles Rams, whose fellow cross-town rivals the Los Angeles Chargers were beaten 22-16 by the San Francisco 49ers.