To Covic's credit he also made two fine saves to keep his side in the fixture.
Shortly after his howler that let Brockie score, the 37-year-old tipped an Alex Smith free kick over the bar that appeared to be destined for the top corner and then got down well to block a Brockie header in the second spell.
The Phoenix won the battle of the midfield which allowed them to enjoy plenty of possession and Manny Muscat was at his combative best for the Wellingtonians throughout the match.
Stein Huysegems was reinstated to the starting XI for the Phoenix, in place of rookie Louis Fenton, in the only change to the side that drew 1-1 with the Perth Glory in Western Australia last weekend.
Huysegems was at his busy best up front for the Phoenix and seems to have an abundance of energy but few chances fell the way of the former Belgian international.
He eventually made way for 17-year-old Tyler Boyd with about five minutes left as Boyd made yet another speedy cameo for the Phoenix but he is still searching for his first goal this year.
Western Sydney, who are in their inaugural season in the A-League, were without midfielder Aaron Mooy who was on international duty with the Australian side.
The visitors lacked penetration in the midfield and Phoenix centre backs Andrew Durante and Ben Sigmund produced decent shifts in defence as they kept the Sydney side in check.
The result means the Phoenix are unbeaten during the past three games and their form spike shows they are well and truly over their recent struggles where they lost three in a row between late October and early November.
The three points also sees them sneak inside the top six.
The Phoenix's next game is on Sunday when they host Alessandro Del Piero and the inconsistent Sydney FC.
Wellington Phoenix 1 (Jeremy Brockie 21)
Western Sydney Wanderers 0 HT: 1-0