Glory, who opened up a three-point gap at the top of the table as a result of Friday's win, were 2-0 to the good when substitute Zadkovich suffered a rush of blood to the head directly after his introduction with 61 minutes gone.
Zadkovich was given his marching orders for a crude challenge on Phoenix midfielder Vince Lia.
Wellington players reacted angrily to the incident and it took referee Lucien Laverdure almost two minutes to calm the situation before brandishing a red card.
Fortunately for Glory coach Kenny Lowe, goals from Daniel De Silva and Andy Keogh proved enough for the home side, although they were given a scare when Roy Krishna pulled one back from the penalty spot with six minutes left.
A sixth victory from the opening seven games of the new A-League season leaves Glory three points clear of Melbourne Victory, who defeated title holders Brisbane Roar 1-0 in the day's other game, despite being well below their best at Etihad Stadium.
Kevin Muscat's team had to wait until late in the second half to finally break the deadlock and needed the assistance of their opponents to do so, Jade North unwittingly guiding the ball home to undo a night of hard work from the dogged visitors.
