While City celebrated their big win, it was a double celebration for their striker Aguero who achieved a milestone; reaching 150 Premier League goals on Sunday.
The Newcastle icon scored a stunning 260 goals in 441 Premier League appearances, a record that will surely live on for some time. These are the type of games where you need to concentrate a lot or you will lose the match.
Two penalties allowed Wolves back into the game and the closing minutes saw backs to the wall defending from Mauricio Pochettino's side to claim and important win.
Chelsea's evolution under the auspices of enigmatic Italian Maurizio Sarri has been seamless.
Chelsea are on the verge of qualifying for the Europa League knockout stages after winning their first three matches despite using Hazard only sparingly in the competition so far. I'm sure with every game and every training session we'll be better and better.
"We couldn't do much against City's quality and sometimes you have to accept that reality", says Shakhtar coach Paulo Fonseca.
Chelsea striker Alvaro Morata has said he is feeling better mentally after coming through a tough spell in his professional and personal life over the past year.
Of course, such mesmerising displays did not go unnoticed, with former Chelsea midfielder Michael Ballack among those to hail Hazard's spectacular form this season.
"With Eden, our doctor says there was no risk in travelling otherwise he would have stayed in Cobham".
'So I think it's normal for a player to play three or four matches and then rest. Now, a year later we are here in England, in London, playing against a top club, and we hope for a better result this time. The good news is Olivier Giroud is fit to return after missing the last two matches with a muscle problem so he should get a recall up front.
Belgium global Hazard returned from two weeks out with a back problem when he came on in the 64th minute of Sunday's 3-1 victory over Crystal Palace.