Lampard scored a penalty won by the Belgian after a good forward run and the former Lille man also provided an assist when he played in Branislav Ivanovic for the Blues' opening goal.
And the 34-year-old, who captained England in their midweek win over Italy, felt that Hazard was key to the comfortable victory for Roberto Di Matteo's side.
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"You saw the quality he brought there with the little spin and putting Ivanovic through and then the speed to get away from his man for the penalty. That's something that I know Chelsea fans are crying out to see and it’s great to play with him.
"You always want to get a win on the opening day and I think coming here, the way they finished the season last year it was a very tough game and we started very well, through this man [Hazard] mainly and it was great football.
"After that it was a pretty even game, it was tough but we always had that lead."
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He claimed: "Branislav's got the legs and the pace to get up there and he's always eager to do that. The link, the turn and the pace, was what made that goal."
Hazard, who joined the Blues for £32 million in the summer after long and protracted negotiations, also admitted his delight to secure a win on his debut.
He said: "Yes I'm very happy. My first game, a win, it’s okay."