It's unlikely, given the early pattern of the contest, that the 12th minute could be looked back upon as a turning point but it underscored the stark differences in execution between the two sides.
City were threatening to run rampant in the opening half an hour as Silva and Sterling went close with speculative shots, and Kyle Walker squandered a good chance when his left foot scuffed a Sane cutback.
Man City continued where they left off in the first stanza, dominating possession, although with a reduced tempo. Kevin De Bruyne put the ball on a plate for Jesus to head home from close range.
Pep Guardiola can clinch his first Premier League title with a victory in next week's Manchester derby after Manchester City's thoroughly comprehensive victory over Everton.
"With the distance we have [16 points], we have to be focused on the Champions League and in the middle we have United - who of course we are going to try and beat and try and play - but the line-up will be thinking about Liverpool".
11 minutes after half time, Fernandinho almost made it 4-0 when his speculative drive from outside the box took a heavy deflection off Calvert-Lewin, wrong-footing Pickford but the England international got a strong palm to the ball to divert it to safety.
That left Wayne Rooney and Morgan Schneiderlin screening the back four, and that duo had neither the pace nor the capability to cope with City's guile and movement, with the former getting the hook just 12 minutes into the second half.
Former Chelsea and Everton star Lukaku, who has netted in five times in his last six appearances, now has 100 career Premier League goals.
The Toffees fans passed a giant print of club legend Howard Kendall, who died in 2015.
With their allegiances different - one supporting the blue of Everton, the other of City - so were their approaches.
City broke quickly again for the third, Silva laying a beautiful pass into the path of Sterling as the game drifted into a training exercise for the remainder of the match. Victory on Saturday would make him the second quickest manager to reach 50 wins in the division, behind Jose Mourinho (63 games). [For] the fans it is significant.
Newcastle beat Huddersfield 1-0 and Watford drew 2-2 with Bournemouth.
And while the Reds needed an 84th-minute winner from Mohamed Salah to get a win at relegation-threatened Crystal Palace, City could hardly have had a more perfect warm-up for their return trip to Merseyside for the first leg in four days' time.
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