The table-topping Bluebirds were second-best until Mackay introduced his £650,000 buy from Sunderland in an inspired 62nd-minute substitution. Young Leeds defender Sam Byram's careless clearance ran to Craig Bellamy whose low shot was expertly turned past Paddy Kenny by Campbell, who was immediately buried by his overjoyed new team-mates.
"I am delighted for Fraizer. He is very humble and has rapidly bought into our team ethic," Mackay said. "He is a willing runner and an intelligent footballer who knows where the goal is. He has not played a lot of football lately so the mind was willing and the flesh was weak, but he will soon be up to speed."
Victory restored Cardiff's 10-point lead over the chasing pack and Mackay was relieved to grab a win against a Leeds side, who toppled high-flying Premier League Tottenham in the FA Cup just last weekend.
"I've never had an easy game at Elland Road in my life and we knew it would be tough today, especially as they had an incredible, very well deserved win against Spurs last week," he said.
"But we applied ourselves really well. David Marshall made an excellent save for us in each half and I will take limiting Leeds to two chances at Elland Road."
Leeds manager Neil Warnock claimed his side should have had two penalties and accused referee Mike Dean of being in a bad position when Cardiff captain Mark Hudson appeared to handle the ball.
"It is a cruel game sometimes. Everything about today was cruel," he said. "We missed open goals and the young lad (Byram) made a schoolboy error. I thought Mike Dean was brilliant but he didn't see the handball, when we all appealed, because he was in a bad position and should have been in a better one.
"He had three or four bodies in the way. The linesman could have helped him out, but they don't, do they. Then there was another handball in the 93rd minute that wasn't given.
"Our two centre-halves were magnificent, we played some good stuff against the top-of-the-table team and were better than them, so it's very frustrating that we got nothing."