It was Elliott's first start in eight games after a spell on the sidelines with a hamstring problem that he had picked up while training with the Republic of Ireland.
The defeat extended luckless Colchester's winless run to seven games. But the result was harsh on Geraint Williams' side as they twice hit the woodwork - heartbreakingly the second time with virtually the last kick of the game when Kemal Izzet smashed his close-range drive off the foot of the post.
The visitors dominated the game for spells but lacked the cutting edge to take advantage as Wolves picked up a fourth win in their last five homes games.
Colchester were really left to rue failing to make their early domination pay when Elliott struck against the run of play.
Mark Yeates tested Wolves keeper Wayne Hennessey after just two minutes and the former Tottenham midfielder then saw his 20-yard drive crash to safety off the post.
Kevin Lisbie was the next to be denied by Hennessey before Johnnie Jackson flashed a free-kick just wide.
Having managed to ride their luck, Wolves stunned Colchester by breaking the deadlock despite the best efforts of goalkeeper Dean Gerken.
Darron Gibson whipped in a left-wing cross that Freddy Eastwood headed goalwards from six yards.
Gerken somehow kept out his point-blank header with a stunning reflex save, but unfortunately for him the rebound flew straight to Elliott who stabbed the ball home from close range.
The impressive Jackson tried to spark Colchester back into life at the start of the second half when his free-kick was deflected wide before Yeates was again frustrated by Hennessey.
But Colchester were lucky not to slip further behind on the hour when Eastwood rattled the post from 25 yards.
It proved to be a rare moment of menace by Wolves and it was Colchester that continued to carry the greater threat with Kevin McLeod forcing Hennessey into a smart 67th-minute save.