Tebow twice overcame third-quarter deficits with a pair of touchdowns to Demaryius Thomas and then engineered a 7-play, 52-yard drive to set up Prater's tying field goal with 1:33 left in the game.
Andre' Goodman intercepted Minnesota's Christian Ponder on the next play and returned it 20 yards to the Vikings' 20-yard line, setting up Prater's game-winning boot.
Tebow also ran for a crucial 2-point conversion, following up last week's last-second 16-13 victory over the Chargers with another such win as the Broncos (7-5) forged a tie with Oakland atop the AFC West.
Denver has taken six of seven games since Tebow took over behind center -- five of them coming by seven points or less.
Ponder finished 29-of-47 through the air and set a team rookie record with 381 yards for the Vikings (2-10).