Sergio "Kun" Agüero had a brace for the hosts at Manchester's Etihad Stadium late on Tuesday.
Already leading 3-2 after the first leg in Gelsenkirchen, City dominated from the start of the contest and virtually all of the action was in front of visiting goalkeeper Ralf Fährmann.
City threatened in the 13th minute, when Kyle Walker's deep pass found Raheem Sterling, who advanced toward the goal and left the ball for Agüero, whose strike hit the post.
Though the penalty looked soft, Turpin felt no need to consult VAR and Agüero coolly converted in the 35th minute to give City a two-goal overall lead.
The Argentine international needed just three minutes to get his second of the night, taking a pass from Sterling and slipping the ball under Fährmann.
With Schalke forced to press forward, City's Oleksandr Zinchenko got the ball to a wide-open Leroy Sane and the German scored against his former club to make it 3-0 on the night and a daunting 6-2 overall in the 42nd minute.
City, despite the more-than-comfortable lead, did not let up in the second half and scored twice in the opening 10 minutes after the re-start.
The first, by Sane, was disallowed for an offside. Sterling's goal in the 56th minute looked set to suffer the same fate until VAR confirmed that all of the attacking players were onside.
Even as City slowed the pace, the nightmare continued for Schalke.
Gabriel Jesus delivered the final blow with six minutes left.
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