Marcus Rashford scored the first goal of the day with a lethal finish in the 23rd minute but Harvey Barnes powered in a stunning equaliser for the hosts just after the half-hour mark.
It looked like United had sealed an 11th consecutive away league game through the mercurial Bruno Fernandes but Jamie Vardy's shot deflected in off of Axel Tuanzebe draw the Foxes level once again as both sides departed with a point.
Story of the Match
Chances from the off
Despite the sleepy Boxing Day setting of the match, both sides enjoyed a bright start. Rashford should have given United the lead instantly as he got on the end of Fernandes' cross but somehow lifted his close range header over the crossbar. Vardy then also went close but he too volleyed an effort over David de Gea's net.
The first goal did eventually come midway through the first period and predictably the orchestrator was Fernandes. From a throw-in on the left-flank, the ball appeared to be running away from the midfielder but he just managed to poke it through to Rashford who converted coolly past Kasper Schmeichel with a low finish for his 50th Premier League goal.
United were not in front for long however, and it was one of the stars of Leicester's season so far, Barnes, who hit the equaliser. Fernandes sloppily gave the ball away to James Maddison, who rolled it inside for his teammate. The winger then took a few touches to control before letting fly with a powerful effort that left De Gea with no chance.
Late goals at the King Power
Following his goal in the first period, Rashford really should have had a second and reinstated United's lead after the break. The England forward managed to get beyond the Leicester defence and set his sights with a powerful effort but Schmeichel managed to stick out a huge paw to deny him.
Whilst Rashford couldn't find a way through, that man Fernandes predictably could, and put the Red Devils ahead again late on. Substitute Edinson Cavani did excellently to turn away from the Leicester midfield and prod a perfect through ball to the Portuguese. Fernandes then showed his trademark skill and composure to finish into the far corner.
With Cavani clambering off the bench to affect the game, Leicester then had their own substitute make an impact. Ayoze Perez was introduced by Brendan Rodgers and managed to drill an excellent ball into Vardy. Positioned practically on the penalty spot, there was no doubt about his finish, with the ball bouncing off of Tuanzebe and finding its way into the net.
As a result of the stalemate, Leicester's first of the season, both sides remain in the top four ahead of another round of Premier League fixtures in a couple of days' time.
Fernandes the inspiration again
There is not much more to say about Bruno Fernandes that hasn't already been said. Since he joined the club almost a year ago, he has so often proven to be the difference for Ole Gunnar Solskjaer's men and that was again the case at the King Power.
He showed a great instinctive touch to prod the ball through to Rashford for the opening goal, whilst his own strike was one of consumate ease. You wonder where the Red Devils would be without Fernandes pulling the strings in midfield.
Leicester a top four contender?
Having now played United, Leicester only have Chelsea to play of last season's top ten. Within those nine matches, they have only lost to Liverpool having beaten every other opponent apart from their two North West foes. The Foxes now seem adept at going to shoulder to shoulder with the best that the Premier League has to offer and at no point appeared overawed.
Whilst a title challenge may be beyond them this campaign thanks to a few shock defeats, these type of results could go a long way in seeing Leicester secure a top-four position.
United denied a record
Solskjaer's men have been one of the Premier League's away experts this season. They had managed to secure 10 consecutive league victories but another was just slightly too much of an ask. It may disappoint that they have just fallen short but that run is still highly impressive.