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.
United star Daniel Penha scored a wonderful goal on the hour mark 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.
Tony Popovic's Victory had gone more than five hours of playing time without scoring before Da Silva struck.
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.
Victory had a Vidmar own goal in the 20th minute chalked off as Da Silva was ruled offside.
United almost scored against the run of play on the half-hour mark when Angus Thurgate forced a brilliant save from Paul Izzo.Â
From the subsequent corner, Thurgate headed home but his goal was erased as Michael Ruhs had fouled Izzo.
Noah Botic then finished with aplomb in the 55th minute but was ruled offside.
Just five minutes later, Ruhs went on a strong run before feeding the ball back to Penha, who swept home with his left foot.
The goal sparked Victory and Arzani's introduction in particular proved inspired, 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 his captain 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.
