Brian Deane headed Leeds ahead before Healy added two more with superb long-range drives as North End struggled.
Richard Cresswell hit back for Preston when he buried a shot into the bottom corner, but Simon Walton made it 4-1 when he swept home a Deane knock down.
Preston reduced the deficit with seven minutes left when Cresswell glanced home Dickson Etuhu's pin-point cross but Leeds deserved to take the points.
Leeds manager Kevin Blackwell
"I'm proud of the players, not only did we win it, but we won it with some
style.
"The signs are that this side is a decent side which just needs time. There
wasn't a player who didn't do what I asked them to do.
"David [Healy] isn't just here to score goals for me. He will be a main contributor to people scoring goals. He is an intelligent man who can play the game at a high level. I have not gone out and signed just anybody."
Preston: Ward, Mawene (O'Neil 45), Lucketti, Davis, Curtis,
Alexander, Etuhu, McKenna, Lewis, Cresswell, Smith (Daley 45).
Subs Not Used: Gould, Lynch, Broomes.
Booked: Cresswell, Davis.
Goals: Cresswell 54, 83.
Leeds: Sullivan, Kelly, Butler, Carlisle, Pugh, Walton, Gregan,
Wright, Oster (Richardson 84), Deane, Healy.
Subs Not Used: Carson, Joachim, Lennon, Kilgallon.
Booked: Carlisle, Sullivan, Healy.
Goals: Deane 13, Healy 15, 44, Walton 72.
Att: 18,531
Ref: C Penton (Sussex).