City students in British Uni quarter-finals
Edinburgh head coach Douglas Samuel said: "We had a good strong squad and in the end it was a comfortable victory and we are really excited and looking forward to the draw for the quarter-finals."
Edinburgh took the lead midway through the second period when Dan Ward swung over a cross which Peder Beck-Friis controlled and hit a low shot into the net from 12 yards. Shortly afterwards, Mark Gair's corner was headed in by substitute Michael Hazeldine.
Leeds scored from the spot four minutes into injury time.
Edinburgh University: Tait, Gair, Scott-Woodhouse, Antoni, Main, MacKinnon, Ward, Milne, Beck-Friis, Craigen, Beacher. Subs: Hazeldine, Murray, Brownie, Gray, Hunter.