Leicester made five changes with Marcus Bent and Craig Hignett given their first full outing, while Leeds also had two debutants in the shape of Brazilian World Cup winner Roque Junior and fellow defender Didier Domi.
The home side took the lead on 20 minutes when Nalis struck a dipping left-foot volley into the top right-hand corner of Paul Robinson's net from 25-yards for his first Leicester goal. An early contender for goal of the season already.
Leeds had no time to get back into it as The Foxes doubled their lead three minutes later when striker Dickov chested the ball down just inside the penalty area and rifled a low right-foot volley that flew past the despairing dive of Robinson.
Leicester looked like adding to their goal tally with Robinson tipping over a header from Scowcroft and full-back Ben Thatcher sending another powerful header against the bar.
Cameroon's Salomon Olembe came on early in the second half before Roque Junior missed what looked a routine clearing header, pulling back Bent and getting cautioned. It could easily have been red.
With 20 minutes to go Reid introduced teenager Aaron Lennon and Lucas Radebe replaced Roque Junior with 10 minutes left.
But the South African defender was at fault as Dickov rounded off a slick passing move to grab his second goal on 83 minutes as Radebe slipped outside the penalty area allowing the Leicester striker to curl a right-foot shot into the net.
Scowcroft wrapped up Leicester's first win back in the top flight by rising unmarked on the edge of the six yard box to head home a Muzzy Izzet free kick for their fourth goal on the stroke of full time. Leeds worst league defeat in over 2 years and a truly bad day at the office.