The Belgian has made just three substitute appearances in the league since returning from an ankle fracture sustained on global duty in June but impressed in the Champions League clash with Atletico Madrid in midweek.
"David is a very important player for us", Conte said.
Hazard has always been linked with a move to Real Madrid and Gerrard explained why performances like last night will invite them to hound Chelsea - just as Barcelona did with Philippe Coutinho this summer.
For Conte's men though, this means less rest and preparation time before Pep Guardiola's in-form City head to Stamford Bridge.
But as City prepare to travel to Chelsea as league leaders this weekend, the landscape for the club could not be more different than it was a decade ago.
There is certainly an opportunity to get back on track well before that though, and next up for the Blues are whipping boys Crystal Palace who have failed to score in all seven games so far this season.
Conte considers this season an opportunity for Hazard to justify such bold claims by making a proper impression on the Champions League and has sensed the player's own determination to hoist his game to a new level.
Former Real Madrid striker Alvaro Morata was a constant threat to Chelsea, forcing a good save from Oblak and seeing another shot go just wide off the coast.
Carlo Ancelotti's double winners that season also recorded the best goal difference (+71) that year and scored more goals at home (68) than any Premier League team before or since.
Conte hinted he was considering fielding the same team as in Madrid after a confidence-boosting result, but there is one enforced change. Midfielder Danny Drinkwater (calf) the only definite injury absentee.
"It was a simple tactical decision", Conte said. I like to watch his games. "But I have to check the physical condition for every single player and then to make the best decision".
'I don't want to know what my players do, ' said the City manager.
"I think our start wasn't so, so easy".
"It was what I wanted and good for me".
Aguero was involved in a auto accident late on Thursday in Amsterdam during his day off when the taxi he was travelling in hit a pillar. Yet Conte expects Hazard to declare himself available with the player eager to make his mark.