The 174th meeting between City and United, which offered little in terms of action, burst into life six minutes from time when Fellaini saw red following a heated altercation with Aguero.
The late flashpoint came after a drab encounter in which Pep Guardiola and Jose Mourinho failed to stake their respective claims for Champions League qualification.
Aguero came closest to deciding the game, striking the post early on and blazing a glorious chance over, after the returning Gabriel Jesus had a goal ruled out for offside in stoppage-time.
But 10-man United clung on for a point that leaves them in fifth, a point and a place behind City with five games remaining.
Mourinho sprung an early surprise at the Etihad Stadium, with the returning Henrikh Mkhitaryan deployed up front with Marcus Rashford and Anthony Martial out wide.
It failed to have the desired effect though, as Aguero turned Kevin De Bruyne’s sumptuous cross against the post in the ninth minute, as City ensured both teams got off to an even start.
Despite going on to dominate the opening quarter, City nearly handed United the initiative when Claudio Bravo needlessly flapped at a Martial cross, but the Chilean goalkeeper avoided another embarrassing moment in an error-strewn season by saving Mkhitaryan’s follow-up.
The pace and directness of Rashford and Martial saw United grow as an attacking threat, but the visitors still needed a world-class save from David de Gea, denying Aguero’s 32rd-minute drive, to keep City at bay.
Aguero turned stand-in centre-back Daley Blind inside out two minutes later but he rashly blazed over the bar, before De Bruyne’s thumping drive drew De Gea into action.
Raheem Sterling burst forward two minutes before the interval but the quality of his finish was found wanting as he too fired over.
United should have taken the lead on the stroke of half-time, but an unmarked Ander Herrera somehow managed to steer Rashford’s free-kick wide from six yards, typifying a frustrating opening period for the Manchester rivals.
Sterling’s finishing was found wanting early in the second period when his tame shot was saved, before Matteo Darmian’s hesitancy when clearing presented Fernandinho with a chance, only for the ball to race clear.
De Bruyne’s deflected drive nestled in the side-netting shortly before the hour as City strengthen their grip on possession and the flow of the game.
Eric Bailly inadvertently blocked Nicolas Otamendi’s goal-bound header on 67 minutes before Sterling managed to test De Gea with a shot four minutes later.
A largely uneventful game erupted seven minutes from time when Fellaini, having just been booked for preventing Aguero from breaking, hauled the Argentine down.
Aguero’s appeals for a second yellow prompted a wild reaction from Fellaini, who threw his head towards the City striker, earning a straight red from referee Martin Atkinson.
City, looking to capitalise on their man advantage, brought on Jesus and the Brazilian sent the Etihad into raptures when headed the ball into the United net in stoppage-time, but the linesman correctly ruled it out for offside.
Aguero then blazed a glorious chance over at the death United held on for a point – how crucial it will be in the race for Europe remains to be seen.
