Here are some of the key points from the game:
Another strong defensive display:
Crystal Palace have clearly been putting in work on their defence in training to make up for Wilfried Zaha's injury with another faultless performance from their backline.
Palace limited title challenging United to only a single shot on target in 90 minutes, showing Roy Hodgson's clear intent to keep their opponents out.
Palace were putting in strong tackles all over the pitch from start to finish, leaving the United players no time on the ball and no space to run forward.
Their regimented positional play kept the United squad from playing their quick passing football and really limited their key players ability to control the game.
The team were on it from the get go, regaining possession when their opponents played any loose passes to their teammates all over the pitch, allowing players such as Andros Townsend and Christian Benteke early half-chances to score.
Vicente Guaita had to make a huge save in the 13th minute, when Nemanja Matic's drive from the edge of the box deflected off a Palace defender and looked destined to loop into the top corner, if not for the keeper's acrobatic dive to claw it out for a corner.
This save seemed to inspire his defenders, who put in a huge performance to keep out the Man United strikers.
Joel Ward reacted quickly to deny Uruguayan forward Edinson Cavani a tap in by intercepting Aaron Wan Bissaka's low cross in the 43rd minute. Gary Cahill and Cheikhou Kouyate's partnership also looks to be growing stronger as both defenders were on the United attackers, blocking and clearing any attempt their opponents made to ruin their clean sheet.
When The Eagles are defending like this, it is hard to see when anyone will be able to get past them with a second straight clean sheet.
A real improvement in attacking play:
Crystal Palace looked completely different to the team that couldn't manage a shot on target against Fulham last week.
The team played some quick and intricate passes around with each other and, especially in the second half, made it very difficult for United players to win the ball off them.
As the game went on, they grew into it, creating some huge chances, and they could've nicked it late on when Patrick Van Aanholt was played through on goal but he was denied by keeper, Dean Henderson, who was quick off his line to close down the angle.
There was also many times when a long ball over the top from the defenders found players on the wing and Christian Benteke was also very good at heading the ball down to his teammates, showing his clear aerial ability. A clear improvement was shown from Roy Hodgson's side and it will be interesting to see how they fare against Jose Mourinho's, Tottenham Hotspur, on Sunday.
Manchester United's lack of quality
At certain points in the first half, it looked like it was going to be a long night for the hosts, with Marcus Rashford firing wide after finding space in the box and Nemanja Matic's powerful drive being acrobatically saved by Vicente Guaita.
However, as the game went on, Man United were having less chances and they were being shut out quickly by Palace defenders.
Their left and right backs weren't getting as much time to find teammates in the box and Bruno Fernandes was limited to playing long passes to the wings towards Marcus Rashford and Mason Greenwood, who were shut out by Joel Ward and Patrick Van Aanholt with great ease.
In the second half, there was almost no threat to the team and it really shows that Manchester United have drawn their last three games. There seems to be a lack of confidence in Ole Gunnar Solskjaer's team who have only managed three wins since they went top of the league earlier this year.
How do Palace approach their next game?
Tottenham Hotspur, fresh off a 4-0 win against Burnley, will be high in confidence approaching this game and they will be looking at this as a good three points in their hopes for top four this season.
However, The Eagles have been very good at keeping their opponents out of late and Spurs might struggle to break through their style of play.
The way Palace played against United, shows that the attack part of this system is improving and an early goal for them might be the best way for them to grab the three points and plunder the spoils back to Selhurst Park.