Leitch-Smith stepped off the bench in the 71st minute to grab all three points for the Alex four minutes later and end the Iron's four-game unbeaten run.
United had looked the more likely to score before goalkeeper Sam Slocombe tipped Luke Murphy's penalty on to the upright and Leitch-Smith buried the rebound four minutes after coming on.
It was Leitch-Smith's first goal since he scored a brace against Stevenage in September and manager Steve Davis hopes the striker is showing signs of getting back to his best following a series of injuries.
Davis said: "Ajay was the only one who reacted to the rebound and fair play to him for being their on hand to drill it in.
"He came on and gave us some life. The injuries take a lot out of Ajay and he is slower to recover than other players so we have to be mindful of that.
"He's always one that we have to wrap in cotton wool and ease in gradually, but he has had a cameo performance here and made a difference with his instinct he has for goals.
"We got a bit of luck with the penalty. It looked dubious, but then it maybe made up for those two we got given against us last week.
"It was a harsh decision from their point of view and maybe a draw would have been fair, but we have nicked it and I am delighted with that.
"We really struggled and I think the only real positives were the three points and the clean sheet."