The visitors took the lead at the start of the second quarter when a Seattle field goal attempt was charged down, allowing Delano Howell to collect the ball and run 61 yards for a touchdown.
Jermaine Kearse soon restored the Seahawks' lead, diving to catch Wilson's second touchdown pass of the afternoon in the end zone.
Adam Vinatieri reduced the deficit to two points with a field goal before half time, but two kicks from Hauschka in the third quarter gave Seattle some breathing space.
That was soon eradicated, however, as Hilton went in for his second touchdown of the match following another Luck pass, although their attempt for a two-point conversion failed.
Seattle edged five points ahead through Hauschka's fourth kick of the match towards the end of the third, but it wasn't enough as Donald Brown rushed for a three-yard touchdown in the final quarter.
The Colts chose to go for another two-point conversion and were successful this time as Luck's pass found Reggie Wayne to open up a three-point gap.
The lead was doubled by a Vinatieri field goal with two minutes left and that proved to be enough as the Colts held out for a memorable victory.