Pep Guardiola came up against his former assistant Mikel Arteta at The Etihad and perhaps not surprisingly it was a tactical encounter won by a calm finish from Sterling. "He showed good character, I am happy for him".
The visitors had gone behind to an early Luke Shaw own goal, but captain Harry Maguire put them level with a header midway through the first half and Aaron Wan-Bissaka and Marcus Rashford added goals in second-half stoppage time to complete the rout.
A late burst of goals gave Manchester United a much-needed 4-1 win at Newcastle United, with Bruno Fernandes making up for a missed second-half penalty by putting his side ahead in the 86th minute.
"Harry scored and leads by example", he added. He had a couple of hard weeks since he last played for us.
"The season started for us today".
Jurgen Klopp's champions were desperate to re-establish their authority after their 7-2 mauling against Aston Villa but were forced to settle for a 2-2 draw after Jordan Henderson's late strike was chalked off for offside.
The pivotal moment came when Virgil van Dijk was on the receiving end of a risky late lunge from Jordan Pickford inside the box minutes early in the game.
The centre-back was injured in a collision with Everton goalkeeper Jordan Pickford and had to be substituted off.
"When I left the pitch, Thiago told me in the red card situation with Richarlison that he thinks he got injured", Klopp said on the Spain global.
Liverpool, with Thiago Alcantara at the heart of everything, were back in front with 18 minutes left when Mohamed Salah volleyed in Yerry Mina's poor clearance to set up a frantic finale, with only Pickford's magnificent save from Joel Matip's header keeping Everton in the hunt.
While the challenge could quite easily have been worthy of a red card, the fact that Dutch defender Van Dijk was penalised for offside by his arm in the initial phase of play meant Pickford didn't even receive a caution.
Thiago, meanwhile, was on the receiving end of a heavy lunge by Richarlison, which resulted in a red card for the Everton forward in the final moment of normal time.
Van Dijk and Thiago will have scans on their knees, as Liverpool seek to assess how severe their injuries are.
Chelsea looked to be in total control after cruising into a 2-0 lead against Southampton at Stamford Bridge, courtesy of two goals from summer signing Timo Werner.
Frank Lampard's rallied immediately to regain the lead, Werner teeing up Kai Havertz for a neat finish to make it 3-2.