Leeds had chances to take the lead early in the first half but City’s Jojo Wollacott saved well from Jordan Botaka and Tom Lyman.
DR Congo winger Botaka went close shortly after, shooting low from the edge of the box but failing to hit the target.
City almost took the lead against the run of play when Marley Bishop raced through one-on-one but was thwarted by keeper Eric Grimes, with the resulting corner headed off the line by Jake Skelton.
But Leeds ran away with the contest after the break scoring three goals in four minutes.
Sloth latched on to Botaka’s through ball and calmly slotted past Wollacott before Mulhern doubled the lead with a cool near-post finish.
The 18-year-old was on hand to add his second and Leeds’ third of the match moments later with a powerful downward header to seal the points for the Yorkshire youngsters.
"Part of my remit is to work with the Under-21s and I only started last week. We've done a few things and they've responded extremely well.
"I saw them play at Millwall last week and we've tried to press on with other things. The reponse has been fantastic and I'm delighted with the win.
"We'll see more when they get a little bit match fitter, but their attitude has been absolutely first-class. Without that, the ability and tactics are worthless."
On Botaka's display, Hart added: "His attitude to the game was terrific. He's a very, very skilful player - that goes without saying.
"Some of the things he did with the ball were really exciting to see. That's the first time I've seen him.
"I work on things like how he approaches the game and he made an excellent first impression."