Pep Guardiola's side bossed the 174th Manchester derby, but a combination of poor finishing and good goalkeeping saw their neighbours come away with a share of the spoils.
The Red Devils were made to hang on in the closing minutes when Marouane Fellaini received his marching orders for a headbutt on Sergio Aguero.
The hosts controlled proceedings which got off to a quiet start, although United were indebted to the woodwork in the ninth minute after they failed to clear a cross into the box.
The ball came out to Kevin De Bruyne on the right and he whipped a low cross towards the right post, where Aguero connected but hit the outside of the right post.
With City seeing plenty of the ball, Jose Mourinho's men looked to play on the counter, but they gave away possession far too often to pose a threat.
After De Bruyne curled an effort into David De Gea's arms from 22 yards out on the left in the 21st minute, Claudio Bravo almost let the visitors in when he palmed a cross from Anthony Martial back into the danger area, but the keeper recovered well to block Henrikh Mkhitaryan's first-time shot from 14 yards out on 24 minutes.
Aguero headed Pablo Zabaleta's cross well wide of the left post on 28 minutes, while he tested De Gea four minutes later with a strike from 22 yards out that the Spaniard caught with both hands to his left, after United had given away the ball once again.
The Argentine striker then created space for himself with a sharp twist and turn on the edge of the box, but his shot did not match the skill as he blazed over on 34 minutes.
Aleksandar Kolarov linked up well with De Bruyne on the left moments later before forcing De Gea to parry his low strike from 19 yards out behind the goal, while Raheem Sterling threatened on 43 minutes as he played a one-two with Aguero in the middle before shooting over from outside the area.
However, United should have taken the lead just before half-time from a free-kick that Rashford delivered on the left, but Ander Herrera steered a free header wide at the back post.
Sterling was quickly out of the blocks in the second half as he cut through the defence in the 46th minute before getting off a left-footed shot that De Gea smothered at his near post.
Aguero did well to dig an effort out from the edge of the box three minutes later that De Gea gathered comfortably, while De Bruyne could only hit the side-netting when he cut inside from the left and saw his strike deflected wide on 58 minutes.
Antonio Valencia was looking out of sorts and a hashed clearance from the Ecuadorian presented a chance for Aguero on the hour mark, but the striker lashed his first-time shot well over the target from just outside the area.
The Red Devils were being pegged back and they had to hang on with just 10 men for the final six minutes when Fellaini lost his head. The Belgian, who had just picked up a booking for a foul on Aguero, brought down the Argentine again 19 seconds later and reacted to the incident with a 'Glasgow Kiss' on his opponent.
Gabriel Jesus was called from the bench in the closing stages and he almost scored a dramatic stoppage-time winner when he headed home Aguero's cross at the near post, but the offside flag halted his celebrations.