Ilkay Gundogan, Bernardo Silva and Sergio Aguero scored within nine minutes of each other in the last 16 first leg tie to almost certainly extend Basel's wait for a first quarter-final appearance in the competition.
Gundogan curled in the fourth from the edge of the area in the 53rd minute as the runaway English Premier League leaders clocked up another emphatic win in their remarkable season.
Basel did their best to make a game of it and created several openings but looked vulnerable every time City attacked.
Meanwhile, Tottenham Hotspur recovered from conceding twice in the opening nine minutes to secure a 2-2 draw away to Juventus in their first leg encounter.
Gonzalo Higuain struck for Juve after two minutes and again from the penalty spot after nine as Tottenham were rocked, but the visitors responded in impressive fashion.
Harry Kane fired home in the 35th minute to halve the deficit -- the first goal Juventus have conceded in 2018 -- before Higuain wasted the chance to score a hat-trick when his penalty on the stroke of halftime hit the crossbar.
Tottenham were rewarded for their endeavour when Christian Eriksen's free kick levelled it up in the 71st minute, meaning the London club will fancy their chances of knocking out last year's runners-up in next month's second leg at Wembley.
