After second-half goals from Tilio and Max Caputo erased Asumah Abubakar's ninth-minute opener at AAMI Park, a deflected strike from Keegan Jelacic in the 69th had City facing a 2-2 draw with the A-League Men cellar-dwellers.
But an unlikely 85th-minute header from Argentine defender German Ferreyra lifted the hosts to a dramatic win on Friday that kept their push for a top-two finish on track.
After what Vidmar called a "very poor" first half from his side, Tilio helped lead City's rally – masterfully bringing down a long ball from Ferreyra and bursting through the Roar's lines to equalise in the 57th minute.
Dogged by injuries in recent years, Tilio has returned to City on loan from Celtic for a second-straight season and while hamstring issues sidelined him for 10 games early on, his form in a current run of eight-consecutive starts earned him a call-up for the Socceroos' recent World Cup qualifiers.
"Selfishly, I'd like to have him another year," said Vidmar.
"From a selfish point of view, if he can play another 30 next year, it will really put him in a better position.
"What I wouldn't want is that if he goes back to Europe again, whether he's at Celtic or he's loaned out, and it's not the right club where he struggles to play or to fit in – it'll be another year lost for him."
Friday's win moved City into second on the ladder, just three behind league-leaders Auckland.
Western United, however, can reclaim their spot on the table away to Western Sydney on Sunday.
The Roar, meanwhile, remain rooted at the foot of the table and need eight points from their remaining four games to avoid setting a new club record for fewest points in a season.
Coach Ruben Zadkovich praised the character of his dressing room during a tough season post-game but, observing City's well-credentialled squad, bemoaned his side's comparative lack of resources.
The under-fire coach initially shrugged off questions on if he felt sufficiently backed before eventually responding "It's quite clear to see, the context is quite clear."
"At some point, there has to be some big decisions made. There has to be a clear direction that we have to take," he added.