Chelsea suffered their third consecutive 0-0 draw (previously drawing with Norwich in the FA Cup and Arsenal in the Carabao Cup) and the performance lacked any ideas, creativity or urgency in attack.
The two Premier League bosses have traded barbs since the new year after Mourinho's comment that he did not feel the need to behave like "a clown" during games touched a nerve with Conte.
If anything, in retrospect view of Ben Chilwell's 68 minute second yellow, the presence of Hazard could have been the decisive factor in ensuring that the game went in favor of the Blues.
Antonio Conte's Premier League winning team have fallen way behind Manchester City and even second placed Manchester United could now extend their lead over the Blues.
Tired Chelsea are feeling the strain from a busy schedule - but there's no let up coming for Antonio Conte's men, writes Peter Smith.More news: Vulgarity used by president projected onto Trump Hotel in DC
"Everything is possible", he said.
Conte, who has been linked with jobs in Italy and with Paris St Germain in France, was then asked if he would resign. I saw Eden (Hazard) was very exhausted so he came off.
Harry Kane became Tottenham's record scorer in the English Premier League by grabbing a second-half double in a 4-0 win over Everton yesterday.
"In the first half Leicester ran more than us, they played better than us. For sure we want to avoid the Mourinho season".
Given the speculation surrounding their manager, it was intriguing to note the response of Chelsea fans.
Chilwell set up Shinji Okazaki, who poked his shot wide before Jamie Vardy, restored to the Leicester line-up following injury, shot into the side-netting. Chelsea's players looked a little exhausted, but our play had good passes and good shifts between play.More news: Institutional Investors Hate on Seagate Technology PLC Falls
Vardy was a constant menace and Conte's defence again failed to corral the England worldwide, who found space to shoot just wide.
And when the Chelsea captain had to be taken off with a hamstring injury in the first half, Christensen was called upon as opposed to Luiz.
Fabregas almost put Chelsea ahead against the run of play, but the midfielder's drive was tipped over by Schmeichel.
The decision to remove Hazard drew jeers from the frustrated Chelsea faithful.
Chilwell was dismissed for two bookable offences, fouling Moses just five minutes after bringing Willian down.More news: English Premier League Wrap 13 January 2018