Leicester imploded defensively as United racked up four goals between the 22nd and 42nd minutes. It was a stylish display from a United side who had entered the game under pressure after losing their last two league games, against Manchester City and Watford, with Chris Smalling opening the scoring after replacing Rooney as captain.
Juan Mata, Marcus Rashford and Paul Pogba, with his first United goal following his world record GBP 89 million (USD 115 million, 102 million euros) arrival from Juventus, were also on target after England captain Rooney was dropped to the substitutes' bench.
It was the second successive Premier League away game in which Leicester had shipped four goals after doing so at Liverpool two weeks ago.
Leicester held their own early on with Robert Huth lashing a shot just over but it was United who edged in front in the 22nd minute after some neat play wide on the left had forced a corner.
It was delivered by Daley Blind and Smalling escaped the Leicester defence to power home a header from six yards.
Ibrahimovic then went close to a goal after collecting a fabulous pass by Pogba, but the Swede's effort on the turn just cleared the bar.
Next it was Pogba's turn to let fly with an outrageous effort from 30 yards that bent towards the top corner but was forced away by Leicester goalkeeper Ron-Robert Zieler.
United finally added a second goal as they turned on the style eight minutes before half-time. Ander Herrera started the move with a fine ball to Mata before a clever pass by Pogba and a fine flick by Jesse Lingard allowed Mata to blast past Zieler.
Leicester made a double change at half-time with key duo Vardy and Riyad Mahrez withdrawn ahead of the Champions League meeting with FC Porto on Tuesday. And they almost had some joy when David De Gea dived at the feet of Islam Slimani but gifted possession back to the visitors with a poor throw.
Fuchs wasted the chance, however, with a poor cross. And at the other end Mata tried to add his second goal with a firm shot that Zieler parried well.
But United were soon back on the attack as Zieler made a smart save from Ibrahimovic. Two more Leicester substitutes combined for what should have been a second goal but Andy King produced a tame shot from a Jeff Schlupp cross and De Gea saved easily.
Gray then went within a whisker of replicating his stunning goal with an almost identical effort which De Gea scrambled back to push over the bar.
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