With the scores locked at 1-1 deep into the game after Gabriel Jesus's opener had been cancelled out by Dominic Calvert-Lewin, City were in need of a moment of magic to change the game.
WATCH: Inside City | Episode 355
It was provided by man-of-the-match Mahrez who curled home an exquisite 71st minute free-kick to restore our lead.
Victory was then confirmed six minutes from time by Sterling who, on his 200th appearance for the Club, lashed home a drive off the bar which was awarded by goal-line technology.
It proved a gripping encounter at Goodison with City also indebted to goalkeeper Ederson who produced an incredible late save, with Pep Guardiola's side 2-1 ahead, to deny Yerry Mina's goalbound header.
But the champions kept our composure to secure a precious three point haul from a testing trip to Merseyside.
View the best of the action in the video above...