"I think we were very lucky ... we could have been 3-1 down at halftime and they deserve a lot of credit for the way they played," Mulvey said.
Perth stayed in the middle of the standings with a 4-2 win over the Wellington Phoenix on Friday.
Glory winger Sidnei Sciola scored twice to help the home side overcome an early 2-1 deficit. His second goal came in stoppage time when Wellington goalkeeper Glenn Moss fumbled a long-range drive from the Perth winger that should have been easily saved.
Referee Matthew Gillett sent Phoenix midfielder Albert Riera off in the 72nd minute after showing him what he thought was a second yellow card of the match.
However, Wellington players told Gillett that he had confused Riera with Louis Fenton, who had received a yellow card earlier in the match. Riera was recalled but substituted a short time later.
On Sunday, the Melbourne Victory host Newcastle to conclude the ninth round.