Kenny McLean nodded in a corner in the 18th minute to give Norwich the shock lead over the reigning Premier League champions on Saturday night.
Norwich were without 10 first-team players through injury but that did not stop them from doubling their advantage as ten minutes later Todd Cantwell made it 2-0 after Pukki broke clear and set him up.
Just before halftime, Pep Guardiola's men got one goal back as Sergio Aguero headed in.
But, there was no stopping Norwich on the day as Emiliano Buendia made the most of Nicolas Otamendi dilly dallying on the ball deep inside City's half to set up Pukki for his sixth Premier League goal.
Rodri's low strike made it 3-2 as City hit back but it was too little too late as Norwich held firm for a win.
City thus suffered a first defeat since January and were five points behind leaders Liverpool who beat Newcastle United 3-1 earlier in the day.
Sadio Mane scored a first-half brace for them as Mohammed Salah was also on target in the 72nd minute. For Newcastle, Jetro Willems scored in the seventh minute to give the team a shock lead.
In another result, Manchester United returned to winning ways riding a Marcus Rashford goal from the spot in the 8th minute against Leicester City.
The result ended Manchester United's three-match winless run.
( With inputs from IANS )