Rashford, who burst onto the scene with four goals in two games last month, delivered for United and under-fire manager Louis van Gaal again to boost the Red Devils' Champions League hopes.
Rashford might also have added a penalty to his 16th-minute goal as he ran the error-prone Martin Demichelis ragged and City again cracked under the pressure in their now apparently doomed Barclays Premier League title bid.
Fourth-placed City, who are now just a point ahead of United and West Ham, did rally in the second half but Sergio Aguero missed a hatful of chances to claim a point
Injuries had robbed them of centre-backs Vincent Kompany and Nicolas Otamendi and their absences ultimately proved costly.
To make matters worse, England internationals Raheem Sterling and Joe Hart joined the casualty list on a tough afternoon, which presents national boss Roy Hodgson with a problem.
The headlines were left with Rashford, who at 18 years and 141 days became the youngest scorer in a Premier League Manchester derby.
The atmosphere was electric and the action frenetic
City made the more positive start with Jesus Navas twice going close, volleying narrowly wide and then forcing David de Gea to save with his feet after some sloppy United defending.
Chris Smalling was booked for pulling back a fired-up Aguero but United quickly matched and then bettered their ferocity.
With Rashford, Anthony Martial and Jesse Lingard in attack, United clearly fancied their chances against City's back-up central defensive pairing and home fans' fears were soon realised.
Juan Mata burst through a gap and slipped in Rashford, who took the ball in his stride and showed a little panache to skip past Demichelis and fire a low shot past Hart.
United might have had another moments later as Martial connected with a powerful shot from distance but Hart saved well.
Demichelis had a chance to redeem himself as he got forward to meet a David Silva free-kick but he headed wide from a good position.
City were forced to take off Sterling with what looked like a groin injury after 26 minutes but Yaya Toure, who pushed forward as a result, went close to an equaliser with a low shot that curled just wide.
Things then started to get a bit heated and even Van Gaal got on his feet to complain after coming together between Aguero and Daley Blind
The pair were to clash again by the corner flag.
The first half ended with two penalty controversies
Firstly as a free-kick was swung into the United box Mangala had his shirt pulled by and Toure felt he was impeded by Carrick as he attempted a shot.
Nothing was given by referee Michael Oliver and he was similarly unmoved when Demichelis appeared to bundle over Rashford just seconds later
United were furious about that decision and tempers were briefly lost in the aftermath.
Demichelis' torture continued into the second half as a poorly hit backpass almost allowed Martial in on goal
To compund matters Hart was injured attempting to clear up the mess and had to be replaced by Willy Caballero
Demichelis did not last much longer as Manuel Pellegrini hauled him off and sent on Wilfried Bony in the hope of saving the game.
Aguero carried the fight back to United and fired a chance over before heading against the post from a Toure cross and then narrowly missing the target with a curling effort.
Aguero was proving hard to handle and Smalling was lucky to escape a second booking for tripping the Argentinian but he could not find an equaliser, shooting wide again late on.
TWEET OF THE MATCH
"Can the ref send Demichelis off pls" - Former City winger Trevor Sinclair (@trevor8sinclair) was less than impressed with Martin Demichelis' efforts before he was substituted in the second half.
PLAYER RATINGS
MANCHESTER CITY
Joe Hart: 7 (out of 10)
Bacary Sagna: 6
Martin Demichelis: 3
Eliaquim Mangala: 6
Gael Clichy: 6
Yaya Toure: 6
Fernandinho: 6
Jesus Navas: 6
David Silva: 6
Raheem Sterling: 5
Sergio Aguero: 6
Substitutes:
Fernando: 6
Willy Caballero: 6
Wilfried Bony: 6
MANCHESTER UNITED
David de Gea: 7
Matteo Darmian: 7
Chris Smalling: 7
Daley Blind: 7
Marcos Rojo: 6
Michael Carrick: 6
Morgan Schneiderlin: 7
Jesse Lingard: 6
Juan Mata: 7
Marcus Rashford: 8
Anthony Martial: 8
Substitutes:
Antonio Valencia: 6
Bastian Schweinsteiger: 6
Timothy Fosu-Mensah: 5
STAR MAN
Marcus Rashford
Took his goal superbly and should have had a penalty
Although he faded in the second half after a lively start, this was another impressive outing from the highly-promising 18-year-old.
MOMENT OF THE MATCH
The opening goal by Rashford provided another delightful moment for the youngster
The teenager showed the composure of a seasoned pro as he took the ball in his stride and left Demichelis groping at thin air on the ground before finishing brilliantly.
VIEW FROM THE BENCH
Most of the game will have looked pretty ugly for Manuel Pellegrini as his City side failed to handle the intensity of United's approach
Injuries disrupted his planning but the enforced deployment of Demichelis at the back always seemed an accident waiting to happen against United's pacy frontline
For Louis van Gaal, this was yet another much-needed result in the nick of time
Every time results have apparently taken him to the brink, he has been able to rouse his side to dig out three points from somewhere.
MOAN OF THE MATCH
Refereeing such games cannot be easy but Michael Oliver did not have his best afternoon
The City penalty appeals may have been debatable but the Rashford one appeared clear-cut
With each high-profile incident, the case for increased use of video technology gets stronger.
WHO'S UP NEXT?
Bournemouth v Manchester City, Saturday, April 2 (Premier League)
Manchester United v Everton, Sunday, April 3 (Premier League)
Source : PA
Source: PA