Sullivan threw for 218 yards and hooked up with Simonds for touchdowns of 79, 19 and 7 yards -- the last one with 2:28 left to play as Colgate (8-2, 4-0 Patriot League) rallied from a 12-point deficit to take the lead.
Lehigh (3-6, 2-2) was able to drive out only to its own 45-yard line before turning the ball over on downs.
Colgate took a 21-6 lead early in the second quarter on a 5-yard touchdown run by Nate Eachus, but Lehigh scored on a 27-yard touchdown pass from J.B. Clark to Sekou Yansane and a 6-yard run by Adam Watson to cut the margin to 21-20 at halftime.
Lehigh seized control with two more touchdown passes from Clark, who hooked up with Mike Fitzgerald on scoring passes of 23 and 39 yards to give the Mountain Hawks a 33-21 lead after Tom Randazza couldn't hit the extra point. It was the second point-after attempt Lehigh missed in the game.
The Raiders responded with a 19-yard touchdown pass from Sullivan with 2:48 left in the third and got the game-winning score late in the fourth.
Clark finished with 338 yards passing and threw four touchdown passes for Lehigh while Fitzgerald had seven catches for 111 yards and Yansane had six for 113. Eachus finished with 103 yards on 26 carries for Colgate.