Gabriel Jesus had a hat trick, but referee Victor Kassai made himself the focus of attention with his inexplicable decision to award a penalty after City's Raheem Sterling went down in the box with the closest Shakhtar player a yard away.
The incident happened in the 24th minute, with the hosts already leading 1-0 on David Silva's goal in the 13th.
Sterling increased the margin to 3-0 in the 48th minute.
Despite the comfortable lead, City continued to press and won another penalty in the 72nd minute, when Silva was brought down in the area. Again, it was Jesus who took the shot to put the English side 4-0 ahead.
Riyad Mahrez, who assisted on Silva's early goal, scored in the 84th minute and Jesus completed the hat trick off the game's final move to make it 6-0.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)