Goals from Lyndon Kane and substitute Jamie McGonigle proved enough to give Coleraine victory and extend their unbeaten Premiership run to 10 games.
Full-back Kane scored from close range after being set up by McGonigle in the 63rd minute, then McGonigle finished a Howard Beverland cross on 65 minutes.
Carrick found the net 10 minutes from time when Aaron Harmon scored from the edge of the box after a Ben Roy cross.
The win sees the Bannsiders move above Linfield into third place in the table.
In the first half, Andrew Doyle almost turned a Neil McCafferty free-kick into his own net, while Daniel Kelly was denied by Michael Doherty.
For the home side, Ian Parkhill glanced a header against the bar and Rodney Brown forced a save from Brian Neeson.
Roy went close to securing a draw for his side in the dying minutes.