Campbell, signed from Sunderland for £650,000, climbed off the bench and scored the only goal of the game on 62 minutes which puts Cardiff ten points clear again.
Young Leeds defender Sam Byram's careless clearance ran to Craig Bellamy whose low shot was smartly turned past Paddy Kenny by Campbell.
"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.
"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 FA Cup win against Spurs last week.
"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."