The Serbia worldwide, a fringe player at Newcastle under Rafa Benitez, left St James's Park in search of regular first-team football ahead of the summer's World Cup finals.
Cairney then finished off a swift breakaway in the second half as the play-off-chasing Blades pushed hard to get back in the game, but instead they allowed the hosts a third successive Championship victory.
Fulham wrapped a 3-0 win and all three points when Tom Cairney swept home the third of the game, as Fulham continue their stunning form, and may have one eye on an automatic promotion spot.
Fourth-placed Fulham have not lost since Mitrovic joined the club on transfer deadline day in January.
"That's the reason why I came here", said the 23-year-old.
"The players enjoy the football more than last season with Newcastle, where we knew how we wanted to play".
"This season, this team, we always try to score more goals than the opponent". We didn't play as much attacking football as we play now. Newcastle was more tactically (set up). "He should be playing at Newcastle", Wilder told reporters after last night's game. "At the end, what I said before, he's a great signing for us and he started well, now he has adapted himself and I believe he is enjoying the rest of the team and we expect he can be better in the games ahead of us", he added. "I want to help my team-mates get promoted this season".