Marcus Rashford marked his 100th United appearance with a ninth-minute winner fashioned by Paul Pogba as two of the men most boosted by Solskjaer’s arrival combined to secure his ninth win at the helm.
United were below their best yet had enough to overcome a flat Leicester display with Claude Puel, the increasingly beleaguered Foxes manager, a target for more vehement criticism from home supporters.
There were no such troubles for Solskaer, whose Midas touch since taking interim charge at United was summed up by two of the men to benefit most from his arrival.
Both Pogba and Rashford had become peripheral players under former manager Jose Mourinho, but Rashford now has six goals and two assists in eight league appearances under Solskjaer with Pogba boasting six goals and five assists in seven games.
After a useful start by Leicester, the first sight of goal came for United, who ought to have made it pay on five minutes.
Nemanja Matic hung a left-footed cross to the far post where the Foxes failed to pick up Rashford, who headed over when he should have hit the target.
Rashford was in a less charitable mood four minutes later, however, as United punished Leicester ruthlessly for a mistake by Ricardo Pereira.
The full-back played a poor pass which was intercepted in midfield by poor Pogba and could only watch as the midfielder lofted a pass beyond the Leicester defence for Rashford.
The striker took a touch before firing a low shot past Kasper Schmeichel.
Leicester finally troubled David De Gea in United’s goal in the 25th minute, when James Maddison collected a pass by Nampalys Mendy and connected with a 20-yard drive.
Yet the effort was too close to De Gea, with the Spaniard making a comfortable save.
Eight minutes before half-time Harry Maguire had a header from a James Maddison corner blocked in a crowded six-yard box, although Leicester’s attempt to pounce on the rebound were halted by the award of a foul.
And Jonny Evans then glanced a header wide of the far post from another corner by Maddison.
Ricardo ended the first half with a decent effort from distance that was held by De Gea and Leicester then began the second half on the front foot.
First Harvey Barnes saw a shot deflected off target before Maddison weaved into the box and drilled an effort low into the side-netting.
But the hosts were unable to maintain their momentum and United threatened just before the hour-mark with Rashford’s long-range shot collected low down by Schmeichel.
Yet moments later came a scare for United from a free-kick struck by Maddison.
It was blocked by the wall but sat up for Jamie Vardy, whose overhead kick was spilled by De Gea, only for the United goalkeeper to grasp it gratefully at the second attempt.
It was shortly afterwards that the home crowd turned on Puel, greeting his decision to replace Maddison with choruses of ‘you don’t know what you’re doing’.
There were moments of late promise for Leicester with Harry Maguire sending a late effort just wide.
But they did not have enough to deny Solskjaer the latest triumph in a quiet revolution that is threatening to transform United’s season.
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