Valkanis was dismissed after 41 minutes after a heated verbal exchange with referee Jarred Gillett.
The incident appeared to spur on his charges, though, as they grabbed the only goal of the game seconds later through Jeronimo Neumann.
Second-placed Victory's hopes of getting back into the contest were stunted by the second-half dismissal of full-back Adama Traore for a rash challenge.
Adelaide winger Iain Ramsay ought to have put the hosts in front after five minutes but spooned a simple chance over the bar from close range.
The busiest man at Hindmarsh Stadium in the opening period was Gillett, who, having cautioned his fifth Adelaide player of the evening, was confronted by Valkanis.
The 38-year-old must have spoken out of turn as he was sent to the stands.
The goal came moments later as Ramsay made up for his earlier profligacy with a teasing run which ended with a cross for Jeronimo to head home.
Former River Plate and Barnsley striker Jeronimo came close to adding a second in the second period but his lob over advancing Victory goalkeeper Nathan Coe hit the post.
Traore's straight red 15 minutes from time further strengthened Adelaide's position but they could not find a second goal, Dario Vidosic missing their best chance when clean through.
The win means Adelaide consolidate fourth spot in the A-League while the Victory remain six points behind leaders Central Coast Mariners.