His treble also equals Alan Shearer's record of eleven Premier League career hat-tricks with his third of the current season.
Manchester City's huge win helped propel them back above their main title rivals Liverpool, as Sergio Aguero's hat-trick, a Raheem Sterling brace and Ilkay Gündogan's long-range effort humbled the Stamford Bridge club.
The three points took Manchester City top of the league - level on points with Liverpool but with a better goal difference.
Watch what went on behind-the-scenes in the video above! .
The Italian manager is in his first season and has Chelsea close to the top four, still alive in the Europa League, alive in the FA Cup and in the League Cup final. The loss left them outside the Champions League places and the pressure is mounting on manager Sarri.
It will require some top management to fix the confidence in the Chelsea dressing room after Sunday afternoon's devastating defeat to Manchester City.
And this was their worst loss in any competition since 1991 after failing to recover from Sterling's fourth-minute opener. Aguero scored thrice despite missing an absolute sitter from a yard out in the first half. Silva had weaved through the area to set up a gilt-edged opportunity but the Argentina forward uncharacteristically poked wide. Chelsea midfielder Ross Barkley inexplicably headed a clearance back toward danger and Aguero pounced by shooting on the turn.
City have now scored 33 goals in their last five home games in all competitions and have a chance of lifting their first silverware of the season when they face Chelsea again at Wembley in the League Cup final on February 24. We had to defend deeper in the last part of the first half. Aguero stepped up and sent Kepa Arrizabalaga the wrong way from the spot.
Likewise, Schalke probably won't have enough to stop a City side in this type of form from taking an important step towards the last eight of the Champions League. And Silva's pass opened the visitors up again for the sixth as he picked out Oleksandr Zinchenko who crossed for Sterling to tap home.
City supporters goaded Chelsea by telling them to bring Jose Mourinho back and, after such a hammering, it may not be long before Stamford Bridge managerial speculation is ramped up again.