The Frenchman struggled for form throughout much of last season, scoring just four goals throughout the campaign, but a goal on the opening day of this season appears to bode well for the former PFA Player of the Year.
Chelsea's John Terry in action with West Ham United's Andy Carroll
Blues captain Terry was quick to hail his teammate's overall performance and impact, telling Chelsea's official website: "He's up there with the very best in the world for me.
"We relied on him too much last season and he can't do it all on his own even though he almost does.
"He's a world-class player and we're very lucky to have him."
Terry also expressed his happiness with the first match under the Conte regime, where a late winner from Diego Costa sealed the points for the West London side after Hazard's opener and James Collins' equaliser for West Ham.
Eden Hazard celebrates after scoring the first goal for Chelsea
"It was very important to get off to a good start," Terry said.
"The way we started and ended last season wasn't good enough by our own standards.
"We said before the game that whether we won lost or drew that was the type of fight and commitment we want from everyone.
"We dug in, it was a big London derby and it means a lot to players and supporters.
"It was great for the management to get off to a good start as well."
With no Champions League or Europa League football for Chelsea this season, all eyes will be on Conte and how he adjusts his team to return to their status as title contenders.
The likes of Hazard will play pivotal roles in ensuring the Blues remain at the upper end of the table throughout the campaign.
Eden Hazard celebrates scoring the fourth goal for Chelsea from the penalty spot