Second half goals from Bernardo Silva and substitute Leroy Sane secured the win as City wore down and eventually outclassed United.
With just three games of the season remaining the Citizens now lead Liverpool atop the table by a solitary point.
And with fixtures against Burnley, Leicester and Brighton to come, Pep Guardiola’s men will now be red hot favorites to claim what will be its sixth ever league crown. City also remains on course to win a treble of the Premier League, FA Cup and League Cup.
For United, defeat leaves it in sixth position in the table, behind both Chelsea and Arsenal in the race to finish in the top four and secure a place in the Champions League next season.
However, there was at least improvement in its woeful performance in losing 4-0 to Everton on Sunday.
Little separated the sides in an opening period that saw few chances and plenty of crunching tackles.
Yet City showed its abundant quality in the second period as it stretched away with United’s players appearing to tire.
Bernardo Silva scored the crucial first goal in the 54th minute, cutting inside Luke Shaw and firing past David de Gea in the United goal at his near post.
United should have leveled immediately, but Jesse Lingard missed the ball when it seemed easier to find the net from Marcus Rashford’s cross.
And United was made to pay for its profligacy as Leroy Sane doubled City’s advantage moments later.
The German international was fed by Raheem Sterling with City breaking away, firing past de Gea who was unable to keep the ball out despite getting a touch.
‘Nothing is played out yet’
Manchester City captain, Vincent Kompany refused to be drawn on the victory’s importance in terms of the title race when speaking to UK broadcaster Sky Sports after the match, instead saying the win was “significant because it’s a derby.”
“In the league, nothing is played out yet. Burnley is a difficult away game next and there is plenty to play for both for us and Liverpool. We will deal with the other games in the next days,” Kompany said.
Guardiola was similarly coy when asked whether the win was a significant step towards the title.
And he said he would be telling his players that there remains much to do in the remaining weeks of the season.
“We have to be a calm. I tell my players not to read or to listen to the TV, just rest and sleep on it,” he told Sky Sports.
‘There’s a difference in quality’
Few City fans will be taking their manager’s advise as they celebrate a third consecutive EPL win at Old Trafford and close in on a potential trophy treble.
Many stayed behind to salute their heroes who celebrated on the pitch as the rest of the stadium emptied rapidly on full-time.
United, meanwhile, is left trying to salvage what has become a hugely disappointing season.
Despite an uptick in form that followed the sacking of Jose Mourinho and temporary appointment of club legend, Ole Gunnar Solskjaer, in December, United has lost seven of its last nine in all competitions.
Solskjaer, who was appointed as permanent manager last month, told Sky Sports he was happy with the effort shown by his team Wednesday but could not deny the best team won.
“We didn’t hit the target too many times but the work rate was there. We just weren’t good enough,” he said.
“There’s a difference in quality — that’s why they are top of the league. They’ve set the standard. Living in Manchester, we can’t be happy with that.”