Heath struck from close range in only the 11th minute to score on his first appearance since joining permanently from Leeds in the summer.
The home defence failed to deal with Mark Yeates' in-swinging free kick, allowing the lanky Heath to nod home from six yards out after Gillingham debutant Alan Julian could only parry Paul Reid's near-post flick.
Gillingham's Simeon Jackson had an immediate chance to restore parity, but Dean Gerken pulled off a fine save from the striker's stinging drive.
Further chances followed for Mark Stimson's men and Nicky Southall was unlucky to see successive free-kicks narrowly evade Gerken's right-hand post as Colchester began to withdraw into their own half.
Despite this, the U's remained a threat on the counter and, with the imposing Clive Platt up front, a second goal was always possible.
The half-time break clearly benefited the visitors more than the home side, who struggled to replicate their first half display.
After U's full-back John White forced Julian to tip over a cross that nearly floated in, Gills boss Stimson chose to ring the changes with a triple substitution on 63 minutes.
Gillingham soon began to attack with greater freedom, but in the 74th minute Julian produced a wonder save to keep out Kemal Izzet's fizzing drive from ten yards and keep his side in the contest.
But Gillingham failed to draw inspiration from their goalkeeper's heroics and the visitors, led by the immaculate Heath, never looked like surrendering their lead.
And when Jackson fired a late effort wide after linking with substitute Gary Mulligan, Colchester knew that victory was theirs.