Marcelo Carrusca broke the deadlock in the 54th minute for the visitors before Juric haunted his former club with an equaliser just six minutes later and then bagged the vital goal in the 80th minute.
The return of striker Jeronimo Neumann and midfielder Carrusca from injury proved vital for the Reds with the Argentine imports combining to open the scoring.
But while the visitors had a decent share of possession, the well-structured Wanderers were mostly able to nullify any threat as Adelaide largely lacked any real spark up front.
It took until the 40th minute for Wanderers goalkeeper Ante Covic to make his first save when Sergio Cirio got his head to a Carrusca ball into the box.
Western Sydney, on the other hand, looked dangerous from the outset.
It took just 35 seconds for the hosts to have their first shot when a Shinji Ono free-kick found Nikolai Topor-Stanley in the box, his ensuing header putting Reds gloveman Eugene Galekovic straight to work.
And the chances kept coming for the Wanderers with striker Juric forcing another save from Galekovic in the 20th minute - the rebound going only as far as fellow new recruit Brendon Santalab who shot just wide.
Juric finally broke through in the 60th minute for his second goal of the season, getting past former Wanderer Tarek Elrich and his superb strike was too good for Galekovic.
Ono was perfectly set up by Italian Iacopo La Rocca to snatch a winner with just over 10 minutes remaining, but the Japanese star sent his shot high.
Instead it was 22-year-old Juric who put the game beyond doubt soon after, heading the ball home off a perfect cross from German Jerome Polenz to send the 16,279-strong crowd into raptures.
Wanderers' coach Tony Popovic said his side were worthy victors.
"It was a tough game but in the end we certainly got the deserved victory," he said.
"I'm very pleased to have come back from a goal behind at home and win the game.
"The players could have easily crumbled under the weight of pressure and expectation but they came back."
Adelaide's new mentor Josep Gombau said while he was unhappy with the scoreline he was pleased with the short-passing, possession-based game his charges displayed - a new style the Spaniard is trying to implement in the side.
"I am satisfied with the work that we did, I think we played good football," he said.
"I thought we could have gotten something from this game but I am happy with how we are playing, we are improving.
"Win or lose for me is not important, what's important is what we are building."
Gombau played down two Wanderers tackles - one by goal-scorer Juric on Isaias and by Polenz on Awer Mabil - that some thought could have been red cards.
"This is just football, he (Juric) scored two goals and he did well, I don't want to talk about the referee," he said.
"This one (Polenz's tackle) maybe, but it's not easy to be a referee, he did what he can."