The 29-year-old headed in the first goal, the ball flicking his hair from Kevin De Bruyne's cross, and struck the penalty with his right foot to make it 2-0, before finishing off Leroy Sane's superb run with his left foot to give City a 3-1 win.
His previous perfect hat-trick came against the same opponents, Newcastle, in October 2015, three of five goals in total that day.
That was also the last time a perfect hat-trick was scored in the Premier League.
Among the 27 are only three current PL players: Peter Crouch, for Liverpool v Arsenal in March 2007; Jonathan Walters, for Stoke City v Queens Park Rangers in January 2013; Romelu Lukaku, for West Bromwich Albion v Manchester United in May 2013.
The others are: Emmanuel Adebayor, Gabriel Agbonlahor, Demba Ba, Andrew Cole, Didier Drogba, Edin Dzeko, Efan Ekoku, Les Ferdinand, Mikael Forssell, Jimmy Floyd Hasselbaink, Thierry Henry, Emile Heskey, Tommy Johnson, Salomon Kalou, Matthew Le Tissier, Steven Naismith, Pavel Pogrebnyak, Mark Robins, Louis Saha, Ole Gunnar Solskjaer, Chris Sutton and Gianluca Vialli.