Favre's pass to Jennings beat corner Dre Bly in Green Bay's first-ever victory in Denver.
Favre threw a 79-yard touchdown pass to rookie James Jones in the first quarter as he totaled 331 yards passing while ending his personal five-game losing streak in Monday night games. The Packers (6-1) have now won 10 of their last 11 games dating back to last season.
Jennings had 141 yards receiving on six catches, while Jones had 107 yards receiving. Ryan Grant led the Packers' ground game, rushing for 104 yards on 22 carries.
Denver kicker Jason Elam put the game into overtime with a 21-yard field goal as time expired.
Favre's TD pass to Jennings came on the first overtime play.