Summer signing Hazard opened the scoring from the penalty spot and then provided an assist for Fernando Torres to seal the points in first-half stoppage time.
The Belgium international has been central to the wins over
"It's not just them two, they have a good link-up with (Juan) Mata and the other midfield players," he said.
"Thanks to the team he (Hazard) has been able to slide in and play very comfortably with the others.
"I know you focus on the goalscorers but I think it was a good performance considering it was our third game in six days. The demand was high playing against tough opposition today."
Torres, 28, was brought down for the penalty and scored a tremendous goal from the edge of the box and Di Matteo is pleased that he has started to add goals to his game once more.
"He was very important for us last season, maybe not scoring as much but providing and working hard for the team," he said.
"He is a great team player as well but it is great to see him scoring and the second goal I think was terrific play from us."
Di Matteo was without captain John Terry today due to a neck injury and the Italian was therefore forced to named a third different central-defensive partnership in succession, but he was pleased with the efforts of David Luiz and Gary Cahill and the defensive performance as a whole.
"That was important today," he said.
"I thought we controlled their threat very well, we didn't concede much to them because if you give space and time to (Demba) Ba, (Papiss) Cisse, (Hatem) Ben Arfa or (Yohan) Cabaye they can hurt you."
Newcastle manager Alan Pardew also acknowledged the performances of both Hazard and Torres.
The two look to be building an understanding at the top of the field for Chelsea and Pardew was very impressed with former Lille man Hazard.
"He is a difficult player because he travels with the ball and buys time and when you have someone who can do that you can time your runs off it," he said.
"He just has a kind of nonchalance about him that marks him out as a great player, every time he got the ball today he made the right decision - he has made a difference to Chelsea."
Torres, who picked up the Golden Boot at this summer's European Championships with Spain, has started the season well and seems to be playing with renewed confidence, something noted by Pardew.
He said: "I thought he was good, I have seen him a few times up close and that was one of his better games that I have seen, certainly the second goal was a classic goal.
"He had some good moments today and it is good for Chelsea that he is playing well."
Pardew's side travelled to Stamford Bridge on the back of a 1-1 draw against Greek side Atromitos in their Europa League qualifier on Thursday night and the former West Ham boss admitted his side were slow out of the blocks against the European champions, but praised their second-half efforts.
He said: "In the first half I genuinely thought we looked a bit lacklustre and lacked a bit of a spark in that period.
"Chelsea were good in that first half and I don't want to take anything away from them but the goals were bad for us - the goal just before half-time was a killer blow really.
"We really had a go second half, we didn't shut up shop or try and cover our losses we tried to get back in it - so I'm fairly positive about my team."