In one of the most one-sided knockout games in the competition's history, City built on their 3-2 away first-leg lead to complete a 10-2 aggregate rout which piles more pressure on under-fire Schalke boss Domenico Tedesco.
Further goals from Raheem Sterling, Bernardo Silva, Phil Foden and Gabriel Jesus put Schalke to the sword in the second half as City sent out an emphatic statement to the rest of Europe and reaffirmed their position as Champions League favourites.
Despite the one-sided nature of the final result, it actually took City a while to get going before their blitz at the end of the first half, with Schalke initially holding firm at the back as City struggled to turn their possession into chances.
Aguero did have one clear opening to break the deadlock after 14 minutes when Kyle Walker's pass sent Sterling to the byline and the winger played a low ball into the middle, but the Argentine could only clip the outside of the post with his finish when he should have done better.
There was little else to shout about for the hosts during the opening half-hour, but they soon moved up the gears and their relegation-threatened Bundesliga opponents had no answer to their increased intensity.
The opening goal came from the penalty spot as Aguero got his first of the night with a cheeky Panenka dink after the referee had adjudged Jeffrey Bruma to have wrestled Bernardo to ground when trying to defend Ilkay Gundogan's clipped pass into the box.
VAR was used to confirm that the penalty was the correct decision, but the video assistant came under scrutiny again moments later when it took almost three minutes to determine that Aguero's second was valid.
The influential Gundogan again began the move with a lofted pass over the top for Sterling, who held off his marker before back-heeling it to Aguero. The Argentine still had work to do, but he kept his balance well to squeeze a finish between the legs of Ralf Fahrmann - his 11th Champions League goal in seven appearances against German opposition.
Aguero's celebrations were delayed by VAR despite the offside decision looking relatively clear-cut on the replay, but City were straight back on the attack after the goal was confirmed and added their third of the night just one minute later.
This time it came down the left flank as Oleksandr Zinchenko played an incisive pass through for Sane, who was left with only the keeper to beat and duly completed the quickfire treble against his former club.
The flurry of goals left City 3-0 up on the night and 6-2 up on aggregate at half time, but they showed no sign of settling for that and were soon back on the front foot in the second half when Gundogan played another sumptuous pass behind the defence for Sane, who this time could only fire his finish wide of the far post.
VAR was back in the spotlight shortly afterwards when it correctly disallowed a second for Sane, but it threatened to be the story of the match when it was called upon yet again two minutes later after the assistant had raised his flag to deny Sterling's goal.
This time the video assistant overruled the on-field decision, though, confirming that the in-form Sterling was indeed onside when he slammed Sane's cultured cross past the hapless Fahrmann.
Schalke managed to hold out for another 15 minutes before City breached their outclassed defence once again with a fluid one-touch move which saw Sane, Foden and Zinchenko all involved before Sane cut the ball back for Bernardo to pick out the bottom corner.
That goal sparked another flurry of three goals in 15 minutes as the hosts continued to show their downtrodden opponents no mercy, with Foden next to get in on the act when he was played through by Sane and rounded the keeper before sliding the ball into an empty net for his first European goal.
Foden almost had a second in as many minutes when he drew a rare save from Fahrmann, but the Schalke keeper was picking the ball out of his net for a seventh time before long as his mistake encapsulated a miserable night for the out-of-form German outfit.
Jesus - on for the two-goal Aguero shortly after the hour mark - whipped a shot goalwards from the edge of the box which Fahrmann should have saved, but allowed to creep under his hand and in.
The referee decided against adding any injury time as Schalke were put out of their misery, but the result leaves Tedesco's job hanging by a thread following a run of five defeats in a row during which time they have now conceded 21 goals.
Man City, meanwhile, march on towards a potential quadruple this season and will now turn their attention to the quarter-finals of the FA Cup as they face Swansea City on Saturday.
MAN CITY (4-3-3): Ederson; Walker, Danilo, Laporte (Delph 72'), Zinchenko; Bernardo, Gundogan, D Silva (Foden 64'); Sterling, Aguero (Jesus 64'), Sane
SCHALKE (5-4-1): Fahrmann; McKennie (Mendyl 74'), Stambouli, Sane, Bruma, Oczipka; Embolo (Skrzybski 69'), Serdar, Bentaleb, Konoplyanka; Burgstaller (Teuchert 79')