A Frank Lampard penalty and a goal from Branislav Ivanovic secured the 2-0 victory but it was the performance of £32 million man which delighted Di Matteo most.
Hazard won the penalty which Lampard scored from following a fine run into the area, and also laid on the pass for Ivanovic who had made a rampaging run forward from right back.
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Midway through the second half Hazard was replaced by Brazilian Oscar for his debut and Di Matteo thought the former Internacional man showed some glimpses of why the Blues decided to splash £25m on him, but that he needs to time to bed in at Stamford Bridge.
"It's going to take a little bit of time,” he said. “It's only our first game and Oscar has only been with us two days really so we need a little bit of time to work them all into our team and integrate them."
The Blues had the game as good as sewn up by half time after their Hazard-inspired first-half showing, and Di Matteo was delighted by the way his side performed.
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"We prepared for the game and the team and we were looking for a good start. It doesn't always happen but I think today they responded very well."
The Italian refused to be drawn on the prospect of Wigan attacker Victor Moses making a switch to Stamford Bridge.
There has been speculation throughout the summer that the former Crystal Palace forward will be making a move back to London, but Di Matteo refused to comment on transfer talk regarding the Nigeria international.
He said: "I don't know, I don't talk about our transfer policy. He's a good player.”