Leroy Sane drilled in the third and picked up a hat-trick of assists after the break as City ran riot.
Sterling, Bernardo Silva, Phil Foden and Gabriel Jesus also scored.
After slotting into the far corner in the first half, Sane set up Sterling with a wonderful curling cross that the England forward smashed into the top corner.
Silva pounced on Sane’s cut-back to make it 5-0 before substitute Foden rounded the goalkeeper after he was played in by the German winger. Jesus made sure he had a slice of the pie with a late curling strike.
City, who came from behind in the first leg in Germany to win 3-2, were knocked out in the quarter-finals of last year’s competition by Liverpool and have never won the Champions League.
The draw for the last eight will take place on Friday at 11:00 GMT.
Manager Pep Guardiola said before this match that City were only “teenagers in the competition” but they were ruthless in this tie and displayed the confidence of seasoned European veterans.
Schalke never looked like scoring and the tie was as good as over the moment Aguero nonchalantly chipped the ball down the middle from the penalty spot.
City were full of creativity and flair – traits epitomised by the fourth goal created by Sane, whose delightful, curling cross was smashed home by Sterling.
The only impediment to City’s progress was a number of time-consuming VAR reviews, which were met with boos from fans inside the Etihad.
Aguero’s second goal was reviewed for over two minutes but Sterling was comfortably onside when Ilkay Gundogan fed a lovely ball in down the right.
Sane had a goal ruled out after he rounded the goalkeeper only to be deemed offside by VAR, and Sterling’s thunderous fourth goal was also reviewed but the correct decision stood.
It was a performance that underlined why City are considered among the favourites to win the competition for the first time.
A number of elite clubs have already been knocked out – Paris St-Germain were outdone by an inspired Manchester United comeback and holders Real Madrid were stunned by Ajax at the Bernabeu.
With one of Bayern Munich and Liverpool certain to drop out on Wednesday evening and Atletico Madrid knocked out by Juventus, Guardiola will be growing ever more confident in the hunt for his third European title.
