United took an early lead after Ricardo Pereira carelessly conceded possession to Paul Pogba, whose chip beyond Leicester's backline was thrashed into the net by Marcus Rashford.
A scrappy period of play followed, with Leicester pressing forward and United coiled to counter-attack, four early yellow cards being administered by referee Mike Dean for cynical fouls as neither side found a way through.
In the second half, though, it was Leicester who emerged with a clear upper-hand, frequently forcing their way into the box before being stifled by last-ditch defending or a fine save from David De Gea.
But despite a tense finale, where Leicester continued to pour forward at will, the breakthrough never arrived and Solskjaer's United stroll on with three points and another clean sheet.
Here are five things we learned from the game.
Soslkjaer's free-roaming groove
The way Ole Gunnar Solskjaer lines up his United side can be deceptive. On the surface, at times, they show hallmarks of the defensive rigidity ingrained into them by Jose Mourinho. A back four, supported by Ander Herrera and Nemanja Matic, who sit back and goad the opposition into opening up and attacking.
But beyond that strong, almost stagnant core, there's a free-roaming fluidity. A license to interchange and buzz freely between positions enabled by that defence. It means that when United do counter-attack, the pace of Marcus Rashford and Jesse Lingard creates a constant whir around opposition defenders, creating the pockets of space which Paul Pogba can inch-perfectly pick out. It's a formula that's worked at Wembley against Tottenham, at the Emirates against Arsenal and now the King Power. No matter what level the opponents, United's once brittle defence sets the lure for every counter-attack and gives the forwards a new lease.
James Maddison the Foxes heartbeat
As United dropped deep and invited Leicester to unpick their defensive blockade, James Maddison was at the core of every Foxes attack. The 22-year old repeatedly dropped into the centre circle to collect the ball from Harry Maguire like a relay routine, swivelled towards goal, drove forwards on a slight diagonal so as to create the angle and looked to feed a through ball to Jamie Vardy or the exciting academy starlet Harvey Barnes.
When upfield on the edge of the United box, Maddison was equally dangerous dribbling into the box and twice came close in the first half with shots from the edge of the area and it was to little surprise that Puel's decision to substitute the playmaker after 60 minutes was greeted by a chorus of boos.
Still young, commanding and dictating with influence beyond his years, he is the player Claude Puel - if the Frenchman is indeed still at the helm - should be building this Leicester side around.
Careless defending leaves Leicester in the lurch
Leicester should’ve already been one behind after just four minutes when Luke Shaw breezed past Leicester's still sleeping defence and floated a ball onto the brow of Marcus Rashford. Perhaps so struck by the sheer easiness of the opening, Rashford somehow steered the header over the bar from all of six yards.
It should've served as a grave warning to the Foxes, but instead they remained rattled in the headlights. Just five minutes later, Ricardo Pereira collected the ball on the corner of the box, looked up for little more than a glance and attempted a through ball towards the centre circle.
All it took was for Paul Pogba to extend one long limb, bringing the ball to an instant standstill, and float a deft chip beyond Leicester’s off-guard defence to Rashford. Take two, and this time the finish was clinical. From thereon, United could sit back comfortably in the knowledge that Leicester would have to open up.
Hours of tactical preparation all thrown to thin air in a matter of minutes thanks to a senseless error, that would go on to shape the entire match.
Sanchez remains a sulk in a sea of smiles
The cathartic lease of life given to United’s squad by Ole Gunnar Solskjaer took slightly longer to seep towards Alexis Sanchez, who seems to have developed into a weary sulk since arriving in Manchester. But after gleefully putting the sword to Arsenal’s fans at the Emirates, Alexis Sanchez earned his first Premier League start under Solskjaer at the King Power.
Would this be the Chilean’s renaissance, the dislodging of the world’s greatest £500,000 per week chip?
What followed though was a return to routine for Sanchez. The surly gesturing, petulantly pointing out teammate’s mistakes, finding reasons to blame blades of grass for his own, waving like a disgruntled driver.
The hope was that a peak had been reached at the Emirates where Sanchez could return to being a formidable star rather than a burdensome extravagance. But on today’s evidence, as he failed to gel with Lingard and Rashford, failing to feed the final ball, often lost in attacks, he looked like a cog out of place in this United side. An unhappy sulk in a sea of smiles brought to an early end after 65 minutes.
Will nervous endings ever take their toll?
How many times can United tempt fate in the final ten minutes? There was no effort from Solskjaer to bolster his side's defence in the once ebbing ten minutes known as 'Fellaini-time'. But with a one-goal lead, just like at Tottenham, and chances spurned by Jonny Evans and a fabulous save from David De Gea to deny a Rachid Ghezzal, Vardy's clearcut chance dribbled on his weaker foot into the goalkeeper's arms.
As the minutes ticked by, the nerves became ever more palpable in a game United might have finished off. The pacey trio receding, Lukaku failing to hold the ball up after coming on and a number of chippy fouls conceded. This time United left, just like at Spurs, with another clean sheet, but eventually a team will find a way to turn over a lead so slender.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies