Boss Brendan Rodgers believes Leicester have proved they can handle themselves at the top of the Premier League.
Marcus Rashford netted his 50th Premier League goal when he opened the scoring before Harvey Barnes struck Leicester's first leveller.
The Foxes remain second, a point ahead of United and subject to other results, but leaders Liverpool now have the chance to stretch their three-point lead when they host West Brom on Sunday.
Leicester had already beaten Manchester City, Tottenham and Arsenal this season and Rodgers feels the point on Boxing Day underlines their credentials.
He said: "We gave them lots of problems and, looking at it, we had some real authority in the game. It shows we are developing and able to compete at the highest level.
"We showed lots of potential last year but with more coaching time and more confidence the players will improve.
"When you play against huge clubs, Liverpool, Manchester United, Manchester City, they have that personality but we played with personality and authority in the game.
"We're nowhere near in terms of budget but from a football perspective we were competitive.
"It was the very least we deserved. We showed real quality and showed we can compete at the level against a team who had won every game away from home."
Rashford was guilty of an awful miss after just 71 seconds when he headed Fernandes' cross over from six yards but made no mistake after 23 minutes.
He found the corner after Fernandes knocked Daniel James' ball into his path but the lead only lasted eight minutes when Barnes fired in from 20 yards.
The visitors dominated large spells of the second half and Kasper Schmeichel denied Rashford another with a fine save.
Anthony Martial had a goal rightly ruled out for offside before Fernandes made it 2-1 with 11 minutes left, latching onto Edinson Cavani's pass.
But the Foxes claimed their first draw in the league this season with five minutes remaining when Jamie Vardy's shot hit Tuanzebe to deflect in.
United boss Ole Gunnar Solskjaer said: "We feel disappointed, the boys are flat. We defended well but they had the one moment at the end, great movement from Vardy and he got a bit lucky and it hit Axel. You can't switch off against quality players.
"We created big chances, it was a good game – end to end – with two teams who are quick on the counter attack.
"We felt we deserved more from the game."
Fernandes' strike was his 14th of the season and he has been directly involved in over half of United's Premier League goals – 31 out of 60 – since his debut in January.
"He is definitely a player who impacts results, he creates chances, scores goals and takes risks," Solskjaer said.
"Any Manchester United player should be brave enough to do that. He is a brave boy and he sees the pass and takes the moments.
"Sometimes I might tear my hair out and say there is an easier pass but you can't take that away from Bruno. You want him to be the X-Factor.
"We all have a role to play and he is playing his to the top of his ability."