After an entertaining but goalless first half, Luke Chadwick put Cambridge United ahead with a smart curling finish on 48 minutes.
Chadwick, who had only come on at half time as a replacement for Ryan Bird, then went off injured just two minutes after breaking the deadlock.
Newport County poured forward in search of an equaliser, but it wasn't until the 90th minute that they drew level.
Yan Klukowski burst down the left and teed up Willmott to side-foot home from inside the area in a dramatic finale to the game.
The result lifts both sides up the League Two table.