Pep Guardiola's side tore Leicester City to pieces 5-1 in the Premier League at the weekend and resumed in similarly menacing mood against the Swiss champions.
Basel were left to rue Dimitri Oberlin failing to punish City's early defensive vulnerability and having a penalty shout turned down as a blistering spell of three goals in the space of nine first-half minutes from Ilkay Gundogan, Bernardo Silva and Sergio Aguero took the game away from them.
Gundogan did his World Cup hopes no harm with a sublime second as Germany boss Joachim Low looked on from the stands and, by the time that showpiece comes around, Guardiola could be reflecting on a history-making return in Manchester.
Throw in a 16-point lead in the Premier League and this coruscating form, and a belief that all things are possible might start to course strongly through the Etihad Stadium.
Oberlin gave an early demonstration of his pace, streaming clear of the City defence before his touch around the onrushing Ederson entirely lacked conviction.
Centre-backs Vincent Kompany and Nicolas Otamendi were unsettled by Oberlin, although penalty claims against the latter found no sympathy from referee Jonas Eriksson.
Raphael Wicky's men undermined such encouraging moments by switching off in their own box and allowing Gundogan to head in Kevin De Bruyne's 14th-minute corner at the near post.
Valentin Stocker was the next Basel forward to almost undo City via the direct route, but the difference in cutting edge was born out once more by Silva's sublime chest control and volleyed finish from Raheem Sterling's chipped 18th-minute cross.
Goalkeeper Tomas Vaclik found himself caught out on that occasion and was rooted to the spot when Aguero seized upon a loose ball to clatter home from 25 yards.
Vaclik regained his poise to scamper out and deny Sterling, but the first half had long become on ordeal for Basel by the time De Bruyne lifted a crisp half-volley narrowly over.
De Bruyne stung Vaclik's palms shortly after the restart, while opposite number Ederson was at full stretch to push Mohamed Elyounoussi's swerving strike around the post.
Seeing De Bruyne and Elyounoussi frustrated in their pitches for the spectacular, Gundogan elected to show them how it was done, curling majestically into the top corner to crown a clockwork move that began with Kompany and Kyle Walker in the City half.
Such a handsome lead allowed Guardiola to give Leroy Sane and David Silva runouts on their returns from injury, with Sterling and De Bruyne afforded a rest.
To their credit, Basel kept asking questions in attack, with Oberlin failing to convert Stocker's cross at the far post and Elyounoussi drilling at Ederson.
Gundogan should have beaten Vaclik from close range to claim the matchball, but his and City's focus remain fixed upon more enduring prizes.
Key Opta facts:
- Manchester City's victory the biggest away win by an English side in the knockout stage of the Champions League (previously Liverpool's 3-0 away victory over PSV in the quarter-finals of the 2006-07 season).
- City have won 34 of their 41 matches in all competitions in this campaign, more than in the entirety of last season (won 33 of their 56 games in all competitions during 2016-17).
- In fact, City have now won 16 of their 21 away matches in all competitions this season, a joint-high across the top five European Leagues, matched only by Paris Saint-Germain (also winning 16 of their 21 away games).
- This is the third consecutive season that City will be going into the second leg of the last-16 stage with a lead, previously beating Dynamo Kiev 3-1 in 2015-16 and Monaco 5-3 in 2016-17.
- This was Basel's first defeat at St Jakob Park in the knockout stages (previously W1 D1) – indeed, they have never gone further than the last 16 (2011-12, 2014-15).