Bastian Schweinsteiger scored his first United goal to cancel out Jamie Vardy's record-breaking strike as the spoils were shared at the King Power.
In an entertaining encounter, Vardy netted for the 11th league game in a row before Basti's header on the stroke of half time meant that United sit third in the league, one point behind new leaders City having missed the opportunity to go top.
The Reds will feel they probably deserved to win have dominated the second half, but surprise package Leicester held out to secure a point and have still only lost once this season.
United were to become the latest victim of Vardy's remarkable scoring spree when he scored for the eleventh game in a row on 24 minutes.
Kasper Schmeichel comfortably claimed Daley Blind's corner and picked out Christan Fuchs in acres of space and the Austrian played through a pinpoint pass for Vardy, whom displayed all the hallmarks of a red-hot striker as he coolly slammed home past David de Gea.
Matteo Darmian arguably should have done more to prevent the goal, but the Englishman peeled away to celebrate as the King Power stood to acclaim the man who had just broken Ruud van Nistelrooy's record to make Premier League history.
Riyad Mahrez was the next to go close for the Foxes when he combined superbly with Shinji Okazaki on the edge of the area and his well-struck effort forced a smart stop from De Gea.
However, just as at Watford, conceding that goal drew a strong response from United and we equalised when Schweinsteiger nodded in from Blind's flag kick on the cusp of the interval.
After half-time, United began to dominate and monopolise possession, but it was Leicester whom repeatedly looked dangerous on the counter.
They almost restored their lead on the hour mark when substitute Leonardo Ulloa forced an excellent save from De Gea after good work from the equally impressive Mahrez.
Reds replacement Memphis should have done better when he lashed over the bar, Vardy was shut out well by Chris Smalling and Darmian fired over late on, bringing to an end a contest in which a draw was probably fair.
Overall team performance: 7/10
United Faithful Man of the Match: Chris Smalling. Vardy got free to score once but was otherwise rendered anonymous. Immense again.