In Victory star Juan Mata's first game against his former club, a 29th-minute penalty from Kosta Barbarouses handed the Wanderers their first win since the Sydney derby on November 29.
The win at AAMI Park, off the back of a standout defensive performance led by Anthony Pantazopoulos, relieved pressure on under-fire Stajcic, while also ending Victory's four-game winning streak.
The Wanderers at least temporarily leapfrog Central Coast - who play Perth on Saturday night - into 11th place, while Victory remain sixth.
"It was a battle for us tonight. We played our 12th game this year and, for me, we probably played better in the other 11," Stajcic said.
"It was one we had to grind out. And sometimes you've got to do that.
"It was one where we had to bunker down. We had the lead, sort of made our own luck in that moment, and showed the character and resilience that we need.
"It's a foundation for the team, but it was good to see it come out when we needed it. And we needed it desperately."
Stajcic wouldn't be drawn on whether the win could be a foundation for a run of improved results.
"I think we've been playing pretty well most games. There's not one game where I walked away, before today, thinking the opposition deserve to win that game," he said.
"But you only get judged on results, and performances are something that we analyse.
"But you need three points - that's what professional football is all about. It was good to show that resilience and determination to get the three points when it probably wasn't our best performance.
"For me, I'd love both. I'm greedy. I want a good performance. I want three points, and hopefully we get that next week."
The Wanderers next play Newcastle at home on Saturday.
Victory were without regular goalkeeper Jack Duncan (delayed onset concussion), and the opening minutes were a scrappy affair.
Stand-in skipper Jason Davidson was booked for a high boot on Brandon Borrello in the 12th minute and will be suspended for Victory's away game against Adelaide next Saturday.
With Roderick Miranda (hamstring), Josh Rawlins (international duty) and Brendan Hamill (knee) still unavailable, Sebastian Esposito and Lachlan Jackson are Victory's only available central defenders.
The Wanderers received a handball penalty when a Borrello shot smacked into Santos's arm and Barbarouses tucked away the spot-kick.
In first-half injury time, Mata broke found Nikos Vergos, but he tamely hit it at Lawrence Thomas.
Pantazopoulos cleared a fierce volley from Mata off the line in the 56th minute, and Santos clipped the outside of the post in the 69th minute.
Victory's debutant goalkeeper Jack Warshawsky denied Bozhidar Kraev at point-blank range in the 79th minute to keep the game alive.
But the Wanderers desperately wound down the clock, while Vergos spurned two chances at the death.
"Definitely not the result we wanted and the performance wasn't good enough," coach Arthur Diles said.
"We weren't at our best again. And in the end we don't deserve to lose the match. We probably didn't deserve to win it either."
