Cazorla was shown a second yellow card for sliding in on Cesc Fabregas and Hazard made the game safe a minute from time with a shot that beat former Chelsea goalkeeper Petr Cech via a sizeable deflection off Calum Chambers.
Branislav Ivanovic was restored at right-back, and as skipper, with Nemanja Matic and Diego Costa also returning to start.
The result lifted Chelsea from 17th into mid-table while Arsenal, who have had three players sent off this week following Olivier Giroud’s dismissal against Dinamo Zagreb on Wednesday, stayed fourth, at least until Saturday’s later matches.
When asked whether the Spain striker should have been more severely punished after he put his hands in the face of Arsenal defender Laurent Koscielny, sparking a fracas that ended with Gabriel’s dismissal, Mourinho gave his backing to Costa.
Mourinho was in feisty form following Chelsea’s much-needed first home win of the season as he slammed his critics in the media for a short-sighted view of the team’s recent problems.
“Two seasons ago we won every match against the title contenders and we were not champions, so I think it’s important because somebody winning means somebody loses points”.
The match kicks off at 7:45 a.m. EST/12:45 GMT and can be seen on NBCSN (US) and BT Sport Europe (UK).
“I don’t use that as an excuse”, Wenger said in a press conference later Thursday.
Wenger shook hands with Mourinho before kick-off, but went straight down the touchline as the final whistle blew and the Blues celebrated only their second Premier League victory of the season.
“For me, it is always in provocation and he uses well the naivety of Mike Dean today”.
How Costa remains on the pitch while Gabriel takes an early bath beggars belief.
How will Jose Mourinho react to Arsene Wenger before Saturday’s game?
“It was just a decision”, he told Sky Sports, having replaced Terry with Zouma on that occasion. He replied: “I don’t know, I leave that to the specialists”.
“I think it’s unacceptable what he does to Koscielny”.
“And in that day we lost the game and the cup [Community Shield]”.