The Belgium midfielder started for the Blues in their 3-2 Community Shield defeat to Manchester City after joining the club earlier this summer.
Di Matteo has brought in several new players to Stamford Bridge this transfer window and was happy with Hazard's performance at the weekend.
"He was lively, he caused them some problems. He had a couple of good opportunities and attempts," said Di Matteo.
"He's playing on the left and finding his feet with Ashley [Cole], but he showed some glimpses of his quality and I'm sure he'll be a big success for us."
Hazard joined Chelsea from Lille for £32m in June.