Two goals from Ilkay Gundogan plus further efforts from the excellent Bernardo Silva and Sergio Aguero saw the Blues, bar a second leg collapse, plant one foot firmly in the next round of the competition.
It was clear from the opening few minutes that FC Basel were going to be handful for the Blues at a packed and noisy St Jakob-Park.
Defending in numbers, the Swiss side were quick on the break and on seven minutes could have opened the scoring when a long clearance saw Serey Die race clear and as Ederson raced out the Basel striker only had to lift the ball over the Brazilian, but his weak effort was easily mopped up by Nicolas Otamendi.
Then Dmitri Oberlin went down under the challenge of Otamendi in the box but referee Jonas Ericsson waved appeals away.
Yet despite the early promise, that was as good as it got for the hosts.
The Blues, who were otherwise dominant, soon unpicked the Basel defence and by the midway point of the first-half, looked to have the game and possibly the tie wrapped up after a devastating 13-minute blitz.
The opening goal came on 12 minutes when Gundogan powered home Kevin De Bruyne’s corner to leave home keeper Tomas Vaclik rooted to the spot.
Four minutes after that a good run and cross by Raheem Sterling found it’s way to Bernardo Silva who teed up the ball before deftly volleying over the keeper and into the top left-hand corner of the net.
City struck again five minutes later as Aguero collected a loose ball 22-yards from goal before unleashing a dipping shot that again left Vaclik rooted to the spot.
Three up and cruising, it was wonderful stuff from a side coming of age in the Champions League.
De Bruyne’s dipping volley and Sterling came close to adding a fourth before the break as the shell-shocked Swiss side struggled stem the sky blue tide.
And it didn’t get any easier for Basel after the break.
Though Mohamed Elyounoussi forced a great fingertip save from Ederson shortly after the restart, the Blues increased the lead just eight minutes in and it was another sublime effort as Gundogan curled home from 20 yards to effectively end the contest.
There were further opportunities at either end - most notably for the Blues when Gundogan looked nailed on to complete his hat-trick only to scuff his effort from six yards and see the danger cleared – but by that stage City had done more than enough.
A dominant performance that equalled the Blues' best in European football away from home, the job is not complete - but it's not far off.
Serey Die’s snatched attempt at a lob with the score at 0-0 cost Basel dearly. The Ivorian badly miscued when the game was finely poised and who knows what a fillip that might have given the Swiss side so early in the game?
Star man: Ilkay Gundogan
Super display from the German who scored twice but could have had four on another night.
What it means…
With the second leg to come in three weeks’ time, City won’t believe this tie is truly over until the end of the tie at the Etihad.
But given City’s four-goal advantage, Pep Guardiola will know his side have one foot firmly in the quarter-finals already.
City make the short journey to the DW Stadium next Monday evening to face Wigan Athletic in the FA Cup Fifth round.
Then it’s the Carabao Cup final against Arsenal the following Sunday as the Blues look to land the first trophy of the Guardiola era.
City become the first English team to Basel in six attempts.
Aguero has scored in all four of City's Champions League away games this season - only Man United's Dwight Yorke can claim to have done the same for an English side,
Aguero's 14 goals in 11 games in 2018 is the best of any striker in Europe's top five leagues.
The 4-0 win equals the Blues' biggest European away win, set earlier this season against Feyenoord.