The beleaguered Phoenix now haven't won in eight games and are stuck third from bottom on the A-League ladder, only a single point ahead of the last placed Mariners.
Wellington dominated possession, but it mattered not as the Mariners racked up an impressive victory.
Garcia came on at half time and wasted little time opening the scoring with a cheeky back heel after the ball fell nicely to him in the box.
Wellington, still shorn of Jeffrey Sarpong and Roy Krishna, struggled to create openings and the Mariners made them pay in serious style.
Roux added a second after latching on to a superb Garcia pass, before Austin iced the cake with a driving finish at Glen Moss's near post.
Blake Powell added a late consolation goal for Wellington, his third goal of the A-League season.
There were question marks over whether Austin's goal should have stood, as Fabio Ferreira was in an offside position, but only aborted his run at the ball long after Louis Fenton had been inconvenienced by it.
Nevertheless, the Mariners move to within four points of the Phoenix, the struggling Newcastle Jets and the resurgent Perth Glory.
Wellington Phoenix 1 (Powell 90+2')
Central Coast Mariners 3 (Garcia 50', Roux 53', Austin 85')
AMI Stadium, Christchurch
Referee: Strebre Delovski
