Chelsea fans have come under increased scrutiny this season following a number of high-profile incidents, including alleged racist abuse of Manchester City's Raheem Sterling last month.
That was followed by a situation at a Europa League match in Hungary, when a section of Chelsea supporters were accused of anti-Jewish chants, reportedly focusing on Spurs.
The two clubs face each other at Wembley on Tuesday and there is expected to be a heightened security presence, with officers reported to be specifically listening out for "hate crime".
Hazard took a lead in urging travelling Chelsea fans to act with respect.
"Just watch the game and enjoy the game. For sure after the game one team will win and one team will lose. Try to be fair," the Belgium international said.
"I like all fans, Spurs also have good away fans. I think it is a good game to play and I hope both fans will enjoy the game.
"Of course [I hope all fans show respect]. These kind of fans [who join in abusive chants] are not fans of football, for me.
"When we are players, we are examples. The fans are also examples. I want Chelsea fans to be the best in the world. I don't want to see a bad image of the Chelsea fans, of course. In football in general, not just Chelsea fans, in Italy we saw a lot of things.
"I want these things to disappear. It's hard because football is a big world, but if we are all together step-by-step, players, managers, journalists, then we can do something. I want people to remember the game."