The ex-Dutch international right back returned to his old hunting ground on Saturday to watch the Londoners go seven points clear at the top of the table with a 2-1 victory over Stoke City.
Hazard opened the scoring for Jose Mourinho's men with a first-half penalty and the Belgium playmaker also laid on the winner for Loic Remy in the second period.
"I am a big fan of Hazard," Melchiot told Reuters in an interview. "Whenever I watch Chelsea play I always feel when he gets on the ball they really start clicking.
"If you look at the way Mourinho has always played with his teams, he always has one star," added the dread-locked Dutchman in reference to the former Real Madrid, Inter Milan and Porto manager.
"If you go back through his history he creates a star and that man is always very, very important and Hazard at this point is the guy he has picked."
Melchiot says Hazard is Chelsea's most creative influence but the collective strength of the team is underpinned by the power of 6-foot-4 (1.94-metre) Serbian international Matic in the holding midfielder's role.
"Cesc Fabregas is one of the architects in the middle but at this point the player who is really important in midfield is Matic," explained the 38-year-old Dutchman who won 22 caps for his country.
"When the towering Peter Crouch came on as a late substitute for Stoke you could see the job Matic was doing to protect Chelsea.
"This team depends on his positioning and the way he makes the team so strong defensively. Then, going forward it's all about Hazard," Melchiot said.
MISS BALANCE
"That's why sometimes they miss a little bit of balance because they also need someone on the right who can create as much difficulty and problems for the opposition as Hazard does on the left."
Neither Chelsea nor Stoke were at their best on Saturday and Melchiot identified the international break as one of the reasons.
"The game started off well for 20, 25 minutes and then it slowed down a little bit," said the Dutchman who made 165 appearances for the London club between 1999 and 2004.
"Sometimes when you see players come back from internationals and they don't get a goal in the first 20 to 25 minutes they can start to struggle.
"I had the same problem when I was playing. It's something that will never go away from the game."
Melchiot has been out of football since retiring four years ago and has no ambitions to become a manager or coach.
"I work for Fox Sports, I enjoy my life, I travel, I talk about the game, I love the game and I will always be part of the game but not as a coach," said the former Ajax Amsterdam, Stade Rennes, Birmingham City and Wigan Athletic defender.
"But if I change my mind it will be to work with children. I love the emotion of a child, to make him or her feel welcomed and loved and to understand the game but when it comes to the top level I just enjoy being a fan."
Melchiot was not planning to visit Stamford Bridge at the weekend but he did so as a treat for his mum.
"I was asked in the morning if I wanted to go to the game and I said no but, I was with my mum, and she really wanted to go so at the last minute I made a call to the stadium and I got one of the best seats," he joked.
"My mum is a very big Chelsea fan. Playing for this team made me who I am today. Wherever I go in the world people recognise me for what I did in England and that started off for me at Chelsea and that's why I will always be grateful to them."
(Editing by Ed Osmond)
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