The England forward struck three times in 11 minutes after Sergio Aguero had netted twice to cancel out Ruslan Malinovskyi's penalty opener for the visitors at the Etihad Stadium.
Here, the PA news agency looks at where Sterling's treble ranks in the list of fastest hat-tricks in the competition.
8 mins: Bafetimbi Gomis
Lyon began their game at Dinamo Zagreb in December 2011 needing a seven-goal swing to advance from the group stages at the expense of Ajax and Gomis scored four goals in total, including his hat-trick either side of half-time, in a 7-1 win. Ajax's 3-0 loss to Real Madrid meant Lyon progressed.
9 mins: Mike Newell
Newell had previously held the record with a "perfect" hat-trick for Blackburn against Rosenborg in 1995. Newell later recalled: "I scored a right-footed shot from outside the box for my first, a header for my second and a left-footed shot for my third. Some people call that the perfect hat-trick but it didn't do us much good as it was the last game in the group stages and we were already out."
11 mins: Cristiano Ronaldo
Ronaldo has scored eight hat-tricks in the Champions League but none faster than against Malmo in 2015 as Real Madrid cruised to an 8-0 victory against their outclassed Swedish opponents. Ronaldo scored his first goal after 39 minutes, his second two minutes after the interval and completed his hat-trick on 50 minutes, before adding a fourth eight minutes later.
11 mins: Raheem Sterling
Manchester City were trailing Atalanta before Sterling set up Sergio Aguero to equalise and the England international was then brought down by Andrea Masiello to allow Aguero to score from the penalty spot. Sterling got in on the act after 58 minutes from Phil Foden's pass and made it 4-1 six minutes later after picking up Ilkay Gundogan's through ball. Sterling completed his hat-trick after 69 minutes from Riyad Mahrez's cross.