Tensions flare at the end of the match as Sergio Aguero and Fernandinho saw red late in stoppage time. "But we accept the red card".
The pair also have history with Aguero having sparked a furore with a two-footed challenge on the Brazilian in the 2013 FA Cup semi-final.
Luiz, meanwhile, whose injury status remains unknown after Aguero's unsafe tackle, said he would not hold a grudge against the players who contributed to the ugly ending of the match. After Hazard had latched on to a long ball from Marcos Alonso to sprint clear of Aleksandar Kolarov and net the third, City's frustration got the better of them as Aguero's wild knee-high lunge on Luiz resulted in furious scenes with all 22 players and staff being involved in a melee.
"They did it, and did it I think quite well, but we didn't win, so we always have something to improve. It is normal in football - when you win you be happy, when you lose you be sad".
The two sets of players clashed by the touchline and Fernandinho could be in serious trouble after grabbing Fabregas by the neck and eventually pushing him with such force that the Spaniard ended up in the crowd.
Players from both sides wore black arm bands in tribute to the 71 people who died in Monday's crash outside Medellin, Colombia.
Stones told the BBC: "In those situations you go in there and back your team-mates up, both teams do that".
Gary Cahill's own goal gave Pep Guardiola's side a deserved lead just before the break as Chelsea failed to hit their recent high notes in the opening period.
Australia secure consolation victory in Adelaide
David Warner and Smith scored 47 and 40 respectively to register their only win in the series and first since February 2016. This effectively negated the absence of AB de Villiers and Dale Steyn plus the loss of form of Hashim Amla.
Italian Conte was thrilled with Chelsea's discipline and character amid the chaos, with even the hot-headed Diego Costa, who equalised with his 11th league goal of the season, trying to act as an unlikely peacemaker during the scuffle.
In the last game of the week, Middlesbrough host Hull City at Riverside Stadium early Tuesday morning.
It was pure opportunism from Chelsea, which was under pressure for much of the game but always looked unsafe on the break with the pace of Hazard and the ruggedness of Costa.
Luiz kept it above board, a very classy gesture to supplement the other gentlemanly action he took for this match.
They are separated by a single point with Everton determined to stop their three-match unbeaten run.
Neither of these bans will be overturned due to the manner in which they were received, and we will have a great chance of coming away from the Etihad with all three points. Fernandinho also had a goal disallowed for offside and Ilkay Gundogan was denied a penalty after a challenge by N'Golo Kante. "Not for the referee", Guardiola said. Let us know by dropping a comment below via our Facebook comment box. We have to stay in this position.
Sunderland climbed off the bottom with a 2-1 win over Leicester. "We hope to keep going in this way".