But this came after the Lions had dominated the early exchanges and taken the lead straight from the kick off when Steve Claridge bundled home a cross from Paul Ifill.
Only two top class saves from Leicester keeper Ian Walker, one to tip over a long-range drive from Steven Reid and then to scramble away Neil Harris' header, stopped the Foxes going further behind.
But once Scowcroft got his head to Jordan Stewart's cross for an equaliser in the ninth minute, City never looked surrendering the three points.
Skipper Elliott headed them in front from Muzzy Izzet's free kick in the 24th minute and a flying volley from Scowcroft almost made the game safe moments later.
A third goal did come shortly after the interval and again it was from a Scowcroft header.
The big frontman stole in unmarked at the far post to power home another Izzet free kick.
Stewart then twice nearly added his name to the score sheet, only to be denied by Tony Warner, before Wise made his sole contribution of note - a foul on Dickov which earned him a yellow card.
Scowcroft then turned provider with a chipped through ball for Dickov to run through, hold off Stuart Nethercott, and finish right footed past Warner.
The humiliation of Wise, coupled with a pre-match announcement of a successful buy-out bid from the Gary Lineker led consortium, poor results for the other promotion chasing sides and the return of long-term injury victim Matthew Jones, made it a good day for Foxes boss Micky Adams.