That huge win puts City back in the title race after a shocking start to the four-game run squeezed into the holiday season and keeps Spurs on the fringes of the chase just six points behind.
City’s victory also means Manchester United were the only side to take maximum points, with Ole Gunnar Solskjaer in charge of his first four games.
Here, AFP Sports looks at five things we learned from the Premier League’s festive fixtures.
Title in Liverpool’s hands
Many expected Liverpool to surrender a slender one-point lead at the top with a tricky trip to Wolves to start and back-to-back games against Arsenal and City to end their festive four-game run.
Yet, it was City who blinked first in the title race with shock defeats to Crystal Palace and Leicester opening up a seven-point lead for Jurgen Klopp’s men on the back of nine straight Premier League wins.
Despite losing for the first time in the league this season at the Etihad, Liverpool remain in pole position with no more meetings against City to come.
“If somebody had told me after both games against Man City we would be 4 points up, I would have paid money,” said Klopp.
City’s key positions exposed
One of the reasons City were red hot favourites to retain their title was the seemingly endless depth of quality on offer to Pep Guardiola.
Yet, the champions’ failure to strengthen in two key positions over the summer has come back to haunt City.
Guardiola wanted Jorginho to compete with Fernandinho in holding midfield but the Brazilian choose to join Maurizio Sarri in moving from Napoli to Chelsea.
When forced to cope without their defensive midfield anchor for the first time this season, City lost to Palace and Leicester.
Similarly, another long-term injury lay-off for Benjamin Mandy has left Guardiola without a recognised left-back with deputies Fabian Delph and Oleksandr Zinchenko exposed defensively and centre-back Aymeric Laporte forced to fill in against Liverpool.
Solskjaer’s immediate impact
Manchester United headed into the festive season under new management, but the appointment of Solskjaer to replace the sacked Jose Mourinho has reaped instant rewards.
A kind fixture list has helped, but United have looked transformed in scoring 14 goals in four wins over Cardiff, Huddersfield, Bournemouth and Newcastle from the side Mourinho left behind, 11 points off a top-four finish.
That gap is now down to six and the turnaround inspired by key players like Paul Pogba and Marcus Rashford hitting top form has also raised hopes United could even spring a surprise against Paris Saint-Germain in the last 16 of the Champions League.
Spurs close but not yet challengers
For much of the festive season Tottenham showed why Mauricio Pochettino is in demand with both United and Real Madrid reportedly poised to make a summer move for the Spurs boss.
The free-scoring form of Harry Kane, Son Heung-min and Christian Eriksen sealed comprehensive wins over Everton, Bournemouth and Cardiff.
However, Tottenham are no closer to the leaders than they started the past four games due to a 3-1 home defeat to Wolves.
Pochettino bemoaned a lack of energy in that defeat and the rigours of four competitions on a stretched squad means even keeping pace with Liverpool and City in the second half of the season is a big ask.
Chelsea lacking firepower
If it wasn’t evident before, Chelsea’s four festive fixtures underlined the need for more firepower up front if they are to secure a top-four finish.
Sarri’s men scored just three goals in four games against Leicester, Watford, Crystal Palace and Southampton.
Eden Hazard scored two of those when playing through the middle at Watford as Olivier Giroud and Alvaro Morata again failed to find the net.
But the Belgian appears happier operating in his favoured position on the left and Chelsea are desperate to do all they can to convince Hazard to extend his current contact that expires in 18 months.
“We played a good match for 80 metres, then we were in trouble in the last 20 metres,” said Sarri after Wednesday’s 0-0 draw against Southampton.
“We have to try to solve the problem. We were in control of every match recently, but it was not easy to score the first goal.”