But, with the pressure mounting in the closing weeks of the season, Chelsea showed nerves of steel as Adam Smith's own goal and strikes from Hazard and Marcos Alonso wrapped up a vital win.
"I don't smell victory yet because there are seven games to go, we have a schedule that's not easy and we know this", the Italian said.
Alonso found the top corner with a curling shot in the 68th minute to ensure that Chelsea maintained their seven-point lead over Tottenham, who had applied pressure on the leaders with a 4-0 rout of Watford in Saturday's early kick off.
"In this instance, following the defeat against Crystal Palace which we didn't deserve, we played [Manchester] City when we might have dropped points, and today we may have dropped points, but instead we won both matches".
The 39-year-old admitted it was hard face a team in such good form, adding: "With the system they play, they do very well with it and they have angles and passing options all over the pitch".
Former Italy boss Conte insisted he relishes the intense pressure surrounding Chelsea's tilt for the title - and even admitted he would crank up the heat on his players himself if necessary.
"I don't know what is necessary to win the league, maybe a bit of luck, but I think this group has massive quality and is very special".
"It is important in every game to try to take three points and this game will be very tough. We must be pleased with the game". Their only win at home came in their first game against them in September 1988. "What we've historically done is always try to win and that's the same aim no matter how many points you have and how many games are left". And we must have the same desire.
Conte revealed after Saturday's game that the key to Hazard's turnaround was his improved confidence, saying: "He is a great player, a great talent and he must understand that he is a great player and never forget this. I think now I can see two teams, Chelsea and Tottenham, in this race", Conte said.
Diego Costa has now gone five Chelsea matches without a goal but it was his shot that Smith deflected in and he went close twice more.