It took City less than two minutes to open the scoring, with Stones's header going through the legs of Tonny Vilhena and into the corner after David Silva had been allowed to deliver the ball from the byline.
By the 10th minute, the Premier League outfit were two goals to the good with Kyle Walker's run being finished off by a sweeping finish from Aguero from an acute angle.
By the quarter-hour mark, it appeared a case of City scoring as many goals as they wished but Feyenoord soon began to improve in the final third, with Steven Berghuis and Michiel Kramer both forcing solid saves out of Ederson, who was wearing head protection after being kicked in the face by Liverpool's Sadio Mane at the weekend.
At this stage, Feyenoord were the better team but City effectively wrapped up the three points as early as the 25th minute when Jesus volleyed into the net on the rebound after Benjamin Mendy's effort had been parried into his path by goalkeeper Brad Jones.
Aguero soon came close to a fourth, instead firing into the side-netting from an acute angle, before Feyenoord picked up three yellow cards in the space of a few minutes as frustration began to get the better of Giovanni van Bronckhorst's men.
City returned for the restart with the attitude that the game had already been won, and Pep Guardiola's charges proceeded to play their hosts out of the match with a period of possession football.
When City did show more ambition, they soon netted a fourth through Stones, who rose above the Feyenoord defence to power a header into the net after meeting Kevin De Bruyne's cross.
Such was the state of the match, Guardiola was able to rest Aguero, Silva and Fernandinho for the closing stages and City still looked the most likely to add a fifth goal of the contest.
Guardiola had to remain content with just the four but this was a statement of intent from City, who have already bettered their record on the road after going through the last European campaign without success on their travels.