The midfielder fired home in the 74th minute to inflict a fourth successive defeat on the rock-bottom Essex club.
Palace were always in the ascendancy and should have taken the lead in the second minute, when teenage forward Victor Moses charged down a clearance and crossed for Tom Soares.
However, the midfielder appeared to panic at the vital moment and guided a side-footed effort over the crossbar.
But the Eagles were not to be denied for long as Phil Ifil was the unlucky defender who diverted the ball into the back of his own net. Danny Butterfield's cross was heading towards James Scowcroft until the full-back intervened when six yards out.
However, Colchester were not behind for long as Kevin Lisbie replied 90 seconds later.
Clive Platt sent his strike partner clear and, after beating Matt Lawrence and Butterfield to the ball, he calmly picked his spot beyond Julian Speroni in the home goal.
The home side refused to be downhearted and always looked capable of finding a winner.
Watson rattled the woodwork with a free-kick in the 31st minute, while Clinton Morrison grazed an upright with a brave header from another quality Butterfield cross.
Morrison had the ball in the net early in the second half, but his effort was chalked off for offside, while Watson found the inside of the post with another dangerous free-kick.
But the highly-rated midfielder was not to be denied as he popped up in the box in the 74th minute to fire a pinpoint Ashley Robinson cross past Dean Gerken to secure the points.
Lisbie did net from close range in the closing stages but he, like Morrison before him, was frustrated by an assistant's raised flag.