The Buccaneers held a 24-7 lead midway through the third period, but the Seahawks rallied for the biggest comeback in team history.
Russell Wilson engineered two straight scoring drives, cutting Seattle's deficit to 24-17 early in the final quarter.
He tossed an interception on the next possession, but Seattle quickly got the ball back and Wilson led the Seahawks on a 59-yard drive, capped by a score-tying, 10-yard TD pass to Doug Baldwin with 1:51 remaining.
On Seattle's second possession in overtime, Marshawn Lynch ran 13 yards to the Tampa Bay 6-yard line, and Hauschka then booted the game-winning kick.
NFC-best Seattle improved to 8-1 for the first time in team history.
The Buccaneers fell to 0-8.