The Belgium international netted his seventh Premier League goal of the season to break the deadlock, converting after finding Ross Barkley's threaded pass.
Barkley scored his first Chelsea goal since his January move from Everton to double the lead in the second half, before Alvaro Morata capped the win in stoppage time following a Hazard assist.
Hazard has now contributed to 11 Chelsea goals this season and therefore is adamant he is in the best form of his career.
"We are enjoying playing well and scoring goals," he told Sky Sports. "The first half was not so easy. They missed big chances and then we have had a bit of luck for our first goal, but we controlled the match in the second half.
"I don't know if I've played better [than I am at the minute], I'm just playing good football because we [Chelsea] are playing good football. I want to keep doing it and keep everyone happy.
"I don't think about personal targets, I'm happy as long as we win. Maybe I need to think about that, some people only think about goals.
"Ross Barkley is playing well. He scored and made an assist. He is doing well and working hard on the training ground."
Maurizio Sarri's side were not regarded as title challengers at the beginning of the campaign but despite their impressive start - the success on the south coast was their sixth in eight games - Hazard has moved to downplay expectations.
"It's too early to be thinking about the title, we know it is tough to win," he added. "But it is good to be up there. We'll maybe watch Liverpool and Man City on the bus."