The brilliant Daniel Arzani delivered two assists off the bench for centre-back Da Silva, who scored in the 95th and 98th minutes to give third-placed Victory a crucial victory on Tuesday night.
In the process, Victory snapped a six-game winless run, plus a five-hour run without scoring.
"It was evident when we scored the first goal you could see Bruno (Fornaroli), Roddy (captain Roderick Miranda), everyone trying to get everyone back to half way," Popovic said.
"There was a belief to get a second, they didn't settle for a draw.
"It doesn't mean you're going to get the winner but you could see the mindset was 'we will get another opportunity' and then it's about taking it.
"Daniel's lay-off was wonderful and I can imagine how fatigued Damien was at that moment to score that goal.
"So to keep it down and score was a wonderful finish for the players, for the club, for the fans. So everyone goes home happy."
United star Daniel Penha scored a wonderful goal on the hour mark, sweeping home with his left foot, but injured himself in the celebrations at AAMI Park.
Penha jumped on top of the LED advertising hoarding, then landed awkwardly and had to come off.
Coach John Aloisi was uncertain how long Penha would be sidelined for and insisted he hadn't seen the celebrations.
United's young defence, which bar 100-gamer Tomoki Imai had just nine games worth of experience, battled bravely.
With Josh Risdon and James Donachie suspended and Ben Garuccio injured, 20-year-old Charbel Shamoon (two games), 19-year-old Kane Vidmar (seven) and 20-year-old debutant Khoder Kaddour held the fort.
"Just really disappointed for our playing group, the club and all of our supporters," Aloisi said.
"Because it's been the story of our season, things haven't gone for us. When we've performed well in most games, we haven't been able to get the results that we deserve.
"But proud as well because we had eight contracted players unavailable and then Penha going off pretty early in the second half. But the young boys, they stood up.
"Disappointed for everyone because I can't question the effort from everyone involved."
Arzani's introduction in particular proved inspired for Victory, as they peppered United's goal time and again without reward.
But with seven minutes of injury time there was always a chance.
Five minutes in, Arzani picked out Da Silva at the back post with a wonderful cross - and he scored a commanding header.
Three minutes later Zinedine Machach found Arzani, who slipped through Da Silva to power a shot into the roof of the net and send their fans crazy.
United next travel to face Brisbane on Friday while Victory host second-placed Central Coast on Sunday.
