The Reds' deserved victory put them at the top of the league table.
The Reds scored four goals and Victory one in 32 breath-taking minutes which opened the Hindmarsh Stadium grudge match.
Victory dangerman Marco Rojas pegged a goal back in the second half but the damage had been done by Adelaide's stunning early raid before a near capacity crowd of 14,115 spectators.
Reds star Dario Vidosic crashed into Victory linchpin Marcos Flores in an opening second ripple which create a punishing physical under-current to the contest.
Within two minutes, emerging Adelaide attacker Evan Kostopoulos scored after his team-mate Fabio Ferreira appeared to lose the ball over the touch-line before passing.
By five minutes, Melbourne's Andrew Nabbout had netted a reply when superbly played into a scoring position by a Rojas dash along the right side.
Adelaide went 2-1 up in the 21st minute when Ferreira scored, benefiting from a precocious volley from Marcelo Carrusca - the gifted Argentine was air-borne when he deftly used the outside of a boot to gift Ferreira the chance.
Just two minutes later, Carrusca himself scored with a sweet, curling left-footer.
And Carrusca provided another goal in the 32nd minute, the boom recruit delivering a pin-point free kick which Kostopoulos headed into the net just metres from goal.
By half-time, there were five goals, six yellow cards and 16 fouls in a tempered affair in searing mid-30 degree heat which prompted a drinks breaks midway through the half.
And Rojas continued the hot theme just two minutes into the second half when he turned a defender inside the box and calmly netted his sixth goal for the season.
Adelaide (22 points) rose to top with the win, though second-placed Central Coast (20 points) can return to the head of the table with a win against Newcastle Jets on Saturday night.
Adelaide United coach John Kosmina praised his players for responding from their loss to Central Coast last Sunday.
"It was an enjoyable victory, but all victories are enjoyable," Kosmina said.
"For me, football is about character as much as it is about football and the guys showed a stack of it to be able to bounce back from a loss last week."
Melbourne Victory coach Ange Postecoglou said his men were completely outplayed by the Reds.
"I don't know if it was a reality check, Adelaide was just too good for us tonight ... but I'm fairly positive about where we are heading," he said.
"The task against a really good attacking team was too much for us tonight."