A cagey first 30 minutes was finally opened up through the individual brilliance of Phil Foden, who fired home from a ball to the edge of the box.
Everton will feel hard done by as the City midfielder's shot ricocheted off the foot of Seamus Coleman, sending Jordan Pickford the wrong way having already committed to his right side.
The Toffees were not behind for long as Lucas Digne's sliced shot cannoned off the post, only for the rebound to be bundled home by Richarlison (not that the Brazilian knew anything about it).
Riyad Mahrez, however, had other plans as the Algerian did what he does best - cut in on his left from the right-wing and curl a beauty into Pickford's far corner, kissing the post as it flew in.
City extended their lead in a somewhat similar style to Mahrez, this time through Bernardo Silva as the winger cut in and fired low at a struggling Pickford. That was enough to kill off Carlo Ancelotti's men and make it 17 consecutive wins for Manchester City.
Midfield role for Foden
With Kevin De Bruyne not fit enough to start and İlkay Gündoğan being given a well-earned break, Foden stepped up alongside Bernardo to control the midfield and be the creative flairs in the side.
A goal just after the half-hour mark could not have been a better start for the 20-year-old, opening the scoring against Everton in what would be yet another important win.
The youngster's maturity on the ball is staggering and has been fairly tipped as one of the most promising prospects in world football.
Although just grabbing the one goal, Foden throughout the match was key to the success at Goodison Park, proving that the Stockport-born Citizen is one of Man City's most indispensable players.
Another record broken
The win in Liverpool meant City are the first side to record 10 consecutive top-flight wins at the start of a calendar year. Wow!
These wins include an impressive performance at Anfield and two dominant displays against Chelsea and Tottenham Hotspur. Pep Guardiola will be happy with the recent performances, but never satisfied and will expect his side to keep pushing.
City are now 10 points clear at the top of the Premier League. Is it possible for a team to catch up?
Battle of the defenders
The only weakness shown against Everton was the effect pushing Joao Cancelo into midfield and Kyle Walker into a winger position could cause for Guardiola and his side.
Having both fullbacks out of position gave Digne and Coleman the freedom of the wings on the counter-attack. This was evident when Digne almost fired in the equaliser for Everton before Richarlison pounced on the rebound for 1-1.
Cancelo pushing into midfield is not usually an issue for City. However, the pace of the Everton fullbacks, mixed with the overload on the wing when Abdoulaye Doucouré adds his technical ability to the attack, caused issues for City and so, meant the score was tied at half-time.
The City manager must have tweaked the tactics for the second half as Everton's only real attacking threat was snubbed for the rest of the game.
Mahrez goes back to his Leicester days
Leicester City fans will have reminisced of Mahrez's time with the Foxes with his fantastic finish against The Toffees on Wednesday night.
The Algerian international was full of confidence as he cut onto his left foot and planted a shot into the far corner, making England's number one keeper look useless - basically a copyrighted move from Mahrez.
Hopefully, his standout performance against Everton will carry into his next games with the winger likely to get a run in the side following an impressive all-round game.
Return of De Bruyne
Despite the win against Everton on Wednesday night taking City 10 points clear at the top of the table, the music to Citizens' ears will be the introduction of Kevin De Bruyne in the 80th minute.
It was evident from the smile on the Belgian's face that he had missed the pitch, and the pitch had definitely missed him.
De Bruyne picked up where he left off with his threading-the-needle passes and unbelievable work ethic, even at 3-1 up.
10 minutes on the pitch was not enough to get the star back on the scoresheet, but it was definitely a positive to see him back after a slightly worrying injury.