The long boot turned back a fourth-quarter rally that saw Seattle erase a 10-point deficit.
The Seahawks forged a 20-20 tie with 1:16 left in regulation on a 53-yard Jeff Reed field goal, but the Broncos then launched a decisive drive starting from their own 23-yard line.
Tim Tebow (6-of-11, 93 yards) got a crucial first down when he scrambled for 19 yards, then picked up 26 more on a screen pass to Lance Ball.
That play set up Hauschka's game-winning kick.
Denver starter Kyle Orton went 16-of-23 through the air of 236 yards, one TD and one interception.
Seattle's Tarvaris Jackson picked up 93 aerial yards on 13-of-22 passing with one touchdown.
2014: The Year in Music [PHOTOS]