The lack of pace of Steve Walsh and Gerry Taggart at the heart of the home rearguard was clinically exposed and only some slipshod finishing prevented Yorke and Cole from finishing with hat-tricks. Leicester also badly missed the physical presence of striker Emile Heskey who was confined to bed with 'flu.
They showed the usual typical never say die spirit which has become part of their trademark under Martin O'Neill. But better sides than Leicester will struggle to halt the wave of attacks and menace shown by United's deadly forward duo in the weeks ahead.
In the second half United looked as if they were going to score every time they broke forward after Leicester had managed to remain on level terms at half-time. The only worrying factor was the continuing uncertain form of goalkeeper Peter Schmeichel who, along with David Beckham, returned after a fortnight's mid-season break.
Leicester made a promising start and a dipping 25 yarder from Steve Guppy almost caught Peter Schmeichel unawares as it flew inches wide. But after 10 minutes United broke the deadlock. Ryan Giggs and Jesper Blomqvist were involved in the build-up before Denis Irwin squared the ball across the area.
Cole's dummy meant that Dwight Yorke was left unmarked at the far post and he made no mistake for his 14th goal of the campaign. Leicester 'keeper Kasey Keller then saved away from his left to keep out a diving header from Giggs following a right-wing cross from Wesley Brown.
Then David Beckham flashed a 25-yard effort just wide as United threatened to take control. But Leicester's fighting spirit dragged them back into the match and Schmeichel came out to save at the feet of Muzzy Izzet before Zagorakis brought them level in spectacular style.
Steve Guppy squared the ball to Zagorakis 25 yards out and his right-footed rocket shot beat the dive of Schmeichel all ends up as it flew into the roof of the net. The Foxes then squandered a golden chance to take the lead when Guppy's left wing centre found Pontus Kaamark unmarked at the far post but from eight yards out he drilled his shot over the bar.
That proved to be costly for United moved up a gear after the break to kill off the game with three goals in 18 minutes. Cole restored the lead for the Red Devils in the 47th minute when he latched onto a long pass from Giggs, outpaced Gerry Taggart and drilled a low cross-shot past Keller.
Cole then shot over from close range after a lack of control by Steve Walsh in trying to cut out a centre from Blomqvist. But it hardly seemed to matter as United added two more goals in double quick time.
First Yorke turned past Walsh and threaded a pass into the Cole whose 61st-minute shot flew under the body of Keller. Then a misjudgement by Keller presented Yorke with his second goal of thegame.
The American tried to shepherd a long ball from Irwin behind the goalline but Yorke nipped in and turned his shot home from a narrow angle. Leicester rallied and in the 73rd minute Walsh gave them a ray of hope when he bundled a fiercely driven cross-shot from Guppy over the line.
But back came United and with six minutes left Yorke completed his hat-trick from close range after Cole's shot had rebounded off a post into his path.
Then in injury-time Jaap Stam completed the rout when he side-footed home Beckham's cross from close range with the Leicester defence again nowhere to be seen.