Hans Vanaken claimed a consolation for the hosts late on but City could have won more comfortably, with substitute Raheem Sterling spurning a couple of good opportunities.
City’s victory was as dominant as they come and in 19-year-old academy product Palmer, they may have unearthed another star.
The youngster, who made a brief appearance against Burnley on Saturday and then scored a hat-trick for the under-21 side later that same day, replaced Kevin De Bruyne in the 65th minute.
He looked every bit as composed as the Belgian playmaker as he took a Sterling pass in his stride and brilliantly beat former Liverpool goalkeeper Simon Mignolet.
It was City’s fourth goal and the game had long been as good as over, however.
The noisy home fans in the steep bowl-like arena could not be quietened but their team was outclassed from the start.
It was also not a distinguished night for the home supporters either. There were loud boos as players of both sides took the knee prior to kick-off and, in further unsavoury scenes that could warrant UEFA disciplinary action, bottles were also thrown at Cancelo as he celebrated the opener.
Having drawn with PSG and beaten Leipzig, Brugge had entered the game with confidence but they were fortunate to keep City goalless for as long as 30 minutes.
Jack Grealish thought he should have had a penalty early on after a challenge by Clinton Mata, Phil Foden fired a dangerous ball through the box and Eder Balanta almost turned the ball into his own net.
Grealish, back in the starting line-up as Sterling again had to make do with a substitute’s role, and Rodri both had goals disallowed.
De Bruyne, returning to his native Belgium for a club match for the first time in nine years, forced a save from Mignolet.
The opener came as Foden lofted a fine long pass into the box and Cancelo got behind the defence to chest down and neatly flick through Mignolet’s legs.
City doubled their lead on the stroke of half-time after Stanley Nsoki blatantly tripped Mahrez just inside the area. The Algerian stepped up to tuck the spot-kick into the bottom corner.
The dominance continued after the break and Walker got on the scoresheet in the 53rd minute as he drilled a low shot through Mignolet’s arms from a De Bruyne pass.
De Bruyne received a great reception from the Brugge fans when he was substituted and Palmer immediately picked up were he left off, finishing after a Sterling break two minutes after coming on.
Sterling himself hit the side-netting and fluffed another shot.
City had their first-choice keeper Ederson back in action but he had nothing to do until having to save a late header from Charles De Ketelaere.
Captain Vanaken followed up with a consolation but City were not done as Mahrez added a fifth from a breakaway.