Watt gave Colchester into a 16th-minute lead, moving forward unchallenged after receiving a pass from Marcus Bean before driving a low 20-yard shot which gave goalkeeper Greg Fleming no chance.
Carlisle's 19th-minute equaliser was created by James Berrett, whose free-kick from the left caused a moment of panic in the U's rearguard. The ball curled awkwardly towards the six-yard line where central defender Magnus Okuonghae poked it past his goalkeeper Sam Walker for an own-goal.
Watt was gifted his second goal in first half added time thanks to a chaotic mix-up in the home defence as the ball ran loose allowing him to take possession, round Fleming and roll the ball into an empty net.
Although Carlisle had plenty of the play they fell further behind in the 67th minute when Luke Garbutt picked out Bean at the far post with a free-kick and he thumped home the header.
Colchester made it 4-1 in the 74th minute when Dominic Vose whipped a shot in from the right and defender Max Ehmer got the last touch as it went in.
Ehmer made some amends with a tap-in at the other end after Walker spilled a free-kick.