Glory entered Friday night's match at HBF Park under the guidance of interim coach Adam Griffiths after David Zdrilic was sacked on Tuesday - just two rounds into the season.
Griffiths made four changes to the starting line-up from last week's 4-0 loss to Melbourne City, with star import Tom Lawrence being the biggest inclusion.
But it was ex-Glory whiz-kid Jelacic who opened the scoring in the 11th minute, before former Chelsea and Manchester United midfielder Mata doubled the lead in the 54th minute.
Mata scored just one goal from 23 appearances for the Wanderers last season, but he ensured his first start for Victory - following on from two bench cameos - was a memorable one.
The win was a strong response for Victory following last week's 5-2 horror show against Newcastle.
Glory remain winless, with just one point to show from three games and the search for a new coach ongoing.
"I enjoyed it. It's been some time since I played from the beginning, so I tried my best to train as hard as I could since I arrived at the club," Mata told Paramount.
"I'm very happy for the Victory. We needed a reaction from last week, last week was not good enough. Today was a very professional performance.
"We deserved the win today."
A moment's of applause was held before Friday night's match to mark the passing of former Glory assistant Alan Vest at the age of 86.
Glory started the match brightly, with Adam Taggart looking dangerous early in combination with star recruit Lawrence.
But it was Victory who drew first blood through Jelacic.
Matthew Grimaldi set up the play by squeezing a pass under pressure to Jelacic, who took one touch to settle before going bang from outside the box.
Glory subbed off Lawrence at half-time, and Victory's lead doubled shortly after when the visitors swung the ball forward for an unmarked Mata to slam home at the far post.
Perth created enough chances in the second half as heavy showers hit the stadium, but they lacked the finishing touch.
On the rare occasions they did get a shot on target, Victory goalkeeper Jack Duncan was up for the challenge each time.
Mata was subbed off in the 70th minute with his side already well on their way to the win.
It marked a significant increase in playing time from the combined 45 minutes he tallied in the first two rounds.
