Substitute Palmer became only the third teenager to score in the Champions League for City, following in the footsteps of Foden and Kelechi Iheanacho, as the youngster curled in a fourth of the evening from the edge of the 18-yard box.
Pep Guardiola's men started with attacking intensity and immediately pegged the hosts back deep into their own half.
The incessant pressure paid off on the half-hour mark, as Phil Foden's exquisite pass found Cancelo, who controlled expertly on his chest and then poked through Simon Mignolet's legs to hand City a deserved lead.
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With the clock ticking towards half-time, City grabbed a second through Mahrez, who won and then coolly converted a penalty, sending Mignolet the wrong way.
The visitors emerged from the interval with a hunger for more goals and the third came in the 52nd minute through Kyle Walker, who fired into the far corner after a perfect De Bruyne pass to finish off a free-flowing passing move.
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Palmer scored the fourth, but with nine minutes remaining, the hosts pulled a goal back through captain Hans Vanaken, however, three minutes later, City were celebrating again as Mahrez tucked in a fifth of the evening.
View all the best images from an exciting encounter via our gallery below.