Hazard and Gonzalo Higuain, making his Stamford Bridge debut, scored two goals each as the Blues eased to three points that moves them back into fourth in the Premier League table.
David Luiz's late fifth added gloss to the scoreline and helped to banish memories of Wednesday's humbling 4-0 defeat at Bournemouth.
Sarri was far from pleased with his side's efforts on the south coast, keeping them in the dressing room after the match for an hour, while he has also been critical of Hazard himself lately, saying the attacker must improve tactically.
After another decisive display for the Blues, though, the attacker expects his coach to be pleased with what he saw on Saturday.
"I always say when we lose a game, we need to win the game after, and we did well," he told Premier League Productions. "We played one of the best games of our season and scored five great goals. The fans were not happy on Wednesday and now they are, so we are happy.
"I think [Sarri] will be happy because he was wanting a reaction from us and we gave him one.
"We are happy and we're looking forward to playing Man City [in next Sunday's EFL Cup final]. We need to keep winning like this. This kind of game is the way the manager wants us to play.
"After this game, our confidence is better than two days ago, but we play the champions [next], so we know it will be difficult. We beat them at Stamford Bridge, so why not again?"
Hazard is confident Higuain's first two goals since his loan move from Juventus will be just the start of a productive partnership.
"We try to work with each other," said the Belgium star. "Higuain is a new player but he knows what the manager wants. He is a great striker and he can score a lot of goals. England is different than Italy and Spain, but he has that ability."