As in recent wins over Southampton and Liverpool, moments of real quality on the break from United were largely swamped by passive periods where they offered very little and were left hanging on to a narrow lead.
Jadon Sancho put the visitors in front in the first-half, capitalising on some dreadful Leicester defending as the Foxes put in a showing worthy of their position at the bottom of the Premier League table.
They improved after the break, without every really looking like scoring, as United moved up to fifth ahead of a real test against table-toppers Arsenal at Old Trafford on Sunday.
Erik ten Hag named an unchanged side at the King Power, keeping faith in those who got the better of Southampton as Cristiano Ronaldo and Casemiro had to settles for places on the bench. James Maddison returned from injury for Leicester.
It was a low-key start overall, perhaps to be expected as two sides more comfortable out of possession and on the counter worked each other out.
A stalemate followed, until United got exactly the situation they wanted. Leicester had plenty of players up the pitch and the visitors pounced, Diogo Dalot playing the ball down the line to Bruno Fernandes who had the freedom of the right wing. He found Marcus Rashford, who slid the ball through to Sancho and the winger calmly went round Danny Ward to leave himself with the simplest of finishes.
United threatened to double their lead before the break, Sancho having a shot blocked and Rashford regularly finding space in between Leicester’s defence and midfield. Even the boos from the home fans that met the half-time whistle lacked energy, summing up a lethargic showing from the hosts.
The Foxes came out for the second-half a better side, unsurprisingly raising the bar from its first-half depths. Maddison had a brilliant free-kick from distance kept out by David de Gea, while Kiernan Dewsbury-Hall had some bright moments dragging his side up the pitch.
Ronaldo and Casemiro were introduced by Ten Hag, the United boss keen to bring some control and ruthlessness and to proceedings. Those changes had the desired impact, with Leicester’s momentum wrestled away.
The visitors had chances to double their advantage, Jonny Evans producing a brilliant piece of defending to prevent Christian Eriksen having a tap-in before Ronaldo’s acrobatic effort bounced just wide.
There was no need for a second goal for United though, as for the third match in a row they did just about enough to get the job done. Focus now turns to this weekend’s clash against Arsenal, a match that will reveal plenty about where both sides are.