Chelsea continued to see more of the ball as the half went on and they almost doubled their lead in the 36th minute, but Cesc Fabregas' free-kick sailed inches over the crossbar.
The Bournemouth loanee was on the receiving end of a convincing 3-0 defeat by the Blues at Stamford Bridge on Boxing Day, extending the Chelsea's winning streak to 12 games.
The former Marseille striker joined the Blues in a £33m deal this past summer, as per The Guardian, but has managed to make just 14 appearances in all competitions with five goals and an assist to show for his efforts.
Antonio Conte has turned Chelsea's and Hazard's fortunes around as the 25-year-old seems to be relishing the freedom given to him on the pitch by the Italian manager.
With Diego Costa and N'Golo Kante suspended, Conte paired Cesc Fabregas and Nemanja Matic in midfield, with Hazard starting up front, flanked by Willian and Pedro.
"I think today we sent a good message", Conte said.
"In four days we have another tough game (against Stoke) and we have to prepare very well".
"They look like champions at the minute, for me, at the moment they're the best team in the league", Wilshere admitted. With these 12 wins in a row we took 36 points and our table is fantastic now.
Chelsea fans will always have a place in their hearts for Jose Mourinho but are also learning to love another Latin coach as Antonio Conte displays the sort of tactical acumen that is steering the club towards the title.
The scar tissue from last season cut deep; Chelsea were flatlining, and after Conte performed his act of resuscitation, he still needed to find solutions for mid-table failure to become credible top-of-the-table fare. "We take game after game and try to win every game", Hazard added.
"We played a good game against Bournemouth, we could have scored more, but I am happy with the attitude of the players".
"Our supporters have seen us work so hard to stop one of the best teams in Europe so we are so disappointed not to see the game out".
Burnley edged away from the danger zone with a 1-0 win over fellow-strugglers Middlesbrough and Sam Allardyce's first match as Crystal Palace manager ended in a 1-1 draw at Watford.
Now they've found that man in Pedro.
Eddie Howe's side rallied round and kept their opponents at bay until half time, but shortly after the restart they fell further behind when Simon Francis brought Hazard down in the box, prompting the referee to award Chelsea a penalty which the Belgian coolly slotted past Artur Boruc.
A long ball from goalkeeper Joel Robles saw Kevin Mirallas score Everton's first goal when his deflected shot beat Kasper Schmeichel, while Romelu Lukaku made it 2-0.
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