Marcus Rashford atoned for his earlier miss with a calm finish from ten yards to give the visitors the lead inside 23 minutes, but the hosts got back level when James Maddison gave a pass to Harvey Barnes, who sent a low stunning shot from 20 yards to beat David De Gea.
Ole Gunnar Solskjaer’s men restored their lead on the 79th minute mark when substitute Edinson Cavani played a perfectly-weighted pass to Bruno Fernandes, who guided the ball past Kasper Schmeichel.
Leicester City once again pulled parity five minutes before the final whistle when substitute Ayoze Perez played the ball into the middle from the right wing and striker Jamie Vardy’s shot took a ricochet off Axel Tuanzebe to beat De Gea.
“I thought it was a good game - two attacking teams and I thought we had lots of really good play. Our defending and counter pressing was very good, you have to do that against teams like Man United they break so fast. In the first half that element of our game was good,” Rodgers said after his side’s stalemate.
"Second half we had to defend a bit more but were still compact and tight and then had good moments when we were playing through and maybe lacked the final pass. We go 2-1 behind and we've always had enthusiasm and confidence but these games you go behind against a team that's been playing so well it really showed the mentality of the players and we deserved a point at least out the game.
"That's Jamie Vardy's game that's why he's one of the best - his concentration level, he'll always be in and around the box. He has a football brain and knows where it's going to drop and then he's there to finish it.
"Marcus Rashford had a chance early on and I thought over the first half we were the better team. Bit of luck went against us and Vardy does what he does, he's a top class finisher. I thought it was the least we deserved.
"Back in tomorrow, recover, then see where we're at we need to look at freshness, lots of players have played lots of games so we'll go back in tomorrow and see where we're at."
