Matthew Grimaldi scored in the 75th minute to make it 1-1, after Craig Goodwin scored the opener for Adelaide in the sixth minute.
The Reds had a goal disallowed for offside moments before Grimaldi's equaliser, and then Victory had a goal of their own waved away for offside in the 88th minute.
It created the platform for Kitto's winning header into the back corner, deep in stoppage time, and caused euphoric scenes on Saturday night as the home side secured a valuable three points and moved up to sixth on the ladder.
Adelaide coach Airton Andrioli wouldn't comment on the controversial finish, instead celebrating the Reds' last-gasp winner.
"I saw our goal in the end, that's the only image I've got in my head at the moment," he said.
"I'm really happy with that ball going in with the last kick of the game, or close to the end, so I can't comment on the disallowed goal."
Their opening goal came after Jonny Yull provided a crisp pass to Goodwin, through much of Victory's defence, releasing the skipper down the left in the early stages of the clash.
Goodwin burst forward, showing terrific control and skill before eventually beating Sebastian Esposito and then chipping the on-rushing Victory keeper Jack Warshawksy.
On 68 minutes the Reds thought they had doubled their advantage, but a great strike from Kitto was chalked off after Goodwin was adjudged offside.
United's leveller came from a lightning-quick counter attack, with strong involvement from their substitutes.
Warshawsky collected a corner from Goodwin, rolled it out for Keegan Jelacic who raced through midfield before releasing Jing Reec.
The striker's shot was too powerful for Smits to control, leaving Grimaldi to tap in past the keeper from close range.
In the dying minutes, Grimaldi thought he'd secured a winner for Victory, picking out the top corner with a shot from just inside the area after being teed up by Mata.
But VAR intervened and Jelacic was deemed to have been in an offside position.
Kitto's winner stood in the 97th-minute after the home side had peppered Victory's penalty area with crosses in search of a winner.
Substitute Juan Muniz then recycled the ball for the Reds and whipped in a cross from the left, with Kitto re-directing the ball with a delightful header to the far post and into the net, past a helpless Warshawsky.
Victory coach Arthur Diles was bitterly disappointed with the disallowed goal.
"I'm very proud of my players, I thought they were outstanding today," he said.
"He (Kitto) scored a good goal and we've got to defend that better, but prior to that we should be up 2-1 and we're talking about a different result."
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