The Reds came from 1-0 down to lead Saturday night's match 2-1 at the break before Victory drew level midway through the second half.
But the visitors' hope was short-lived with United finding the winner on 71 minutes.
Victory were the dominant side from the outset and deservedly opened the scoring on 17 minutes through Ryan Teague.
The Reds coughed up possession on halfway and, after being involved to recover the ball, Teague latched onto a delightful through ball from Bruno Fornaroli before coolly dispatching from 10 metres.
Victory almost added a second minutes later when Santos drove towards the box before squaring a pass across the area for Daniel Arzani whose powerful low shot was well saved by the legs of Ethan Cox, in just his second A-League match.
With the temperature still in the low thirties, referee Alireza Faghani called for a drinks break midway through the first half.
It appeared to turn the tide in Adelaide's favour and the hosts equalised on the half hour.
Panagiotis Kikianis lifted a ball over the Victory defence for Stefan Mauk who had ghosted through the visitors' back four, with the United midfielder slamming a half-volley past Jack Duncan.
Stefan Mauk scores for Adelaide United. (Matt Turner/AAP PHOTOS)
Shortly after, former Victory attacker Ben Folami was released by Zach Clough but his shot from just inside the area was tipped over by Duncan.
Just as the half ticked over 45 minutes, United took the lead courtesy of an own goal.
Dylan Pierias was released down the right by Kikianis and the Reds fullback whipped in a low cross.
Victory stopper Brendan Hamill was first to the contest, but cleared straight into the path of the sliding Roderick Miranda, with the ricochet beating Duncan at the near post.
The visitors were first out of the blocks following the interval and Santos should have done better with his chance on 48 minutes, skying over the bar from close range after being slipped through by Zinedine Machach.
The Brazilian made amends though, scoring a classy equaliser to make it 2-2 on 65 minutes.
Arzani whipped in a cross from the right which evaded everyone except Santos who was charging in at the far post and knocked the ball into the net with a diving header.
Following Victory's goal, referee Faghani called for a drinks break and, just as it was in the the first half, it proved the circuit break the Reds needed.
Within two minutes of restarting, United regained their lead.
A long ball from Jay Barnett on halfway found Clough out wide on the left who slipped through substitute Yaya Dukuly.
The pacey winger drove to the byline before cutting back to the penalty spot where Ethan Alagich's first time shot hit a couple of Victory bodies before nestling into the net.
