Cristiano Ronaldo, who left Premier League side Manchester United on Tuesday, had smashed a teenage fan's phone after a defeat at Everton after a Premier League game last season.
Real Madrid's record goalscorer hit 450 for the Spanish giants, while he scored 101 times for Juventus and five for Sporting Lisbon.
Juergen Klopp's Liverpool side went into the game, their first competitive match in 103 days, knowing a victory would allow them to secure their first league title in 30 years on Wednesday with a win at home to Crystal Palace.
Responding to an initiative already run by fans of both clubs, City and United will donate 50,000 pounds each to the Trussell Trust, a support network of more than 1,200 food banks.
Everton said the club and Kick It Out had received reports of a homophobic chant being aimed at Chelsea’s fans by a small section of the home crowd during Saturday’s match.
Liverpool surged eight points clear at the top of the Premier League as Divock Origi was the scourge of Everton once more in a thrilling 5-2 Merseyside derby win for the European champions at Anfield.
Santiago Solari marks his 100th day in charge of Real Madrid with a 1-1 draw at Barcelona in the Copa del Rey, 101 days after his predecessor's reign ended with a 5-1 thrashing to the Catalans.
Tottenham Hotspur were the only team not to bring in a single player during the transfer window.
A 14th straight victory for City is a record run in a single top-flight season while Liverpool were off the mark as Wayne Roney equalised for Everton.
The 31-year-old signed a two year contract on a free transfer bringing the curtain down on 13 trophy-laden years at Old Trafford.
Arsenal joined Manchester City at the top of the Premier League on Saturday after leaders City suffered another afternoon of woes.
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