Chelsea response pleases Hazard
Spurs started best in the London derby at Stamford Bridge, and could have taken the lead when Harry Kane headed against the crossbar.
The Premier League leaders quickly got going, though, with Hazard's 19th-minute strike paving the way for their 3-0 victory.
Didier Drogba quickly doubled that advantage before substitute Loic Remy sealed the three points 17 minutes from time as Chelsea maintained their six-point lead atop the table.
That gap was eight before last weekend, when Chelsea were held to a goalless draw at Sunderland and second-placed Manchester City won at Southampton, and Hazard felt bouncing back was crucial.
"It was important to win today because we lost two points last week against Sunderland," the Belgian said.
"We want to stay on top. Today was a very good match, I think. We played very good. It was important.
"Through the first 15 minutes, [it] wasn't good. After the start, we did very well. We created a lot of chances and we scored three beautiful (goals).
"We have six points in front ... and we want to stay there."
Hazard also praised Drogba's contribution during the victory, after the Ivorian helped set up the opener before getting on the scoresheet himself.
Drogba led the line in Diego Costa's enforced absence through suspension, and Hazard said: "He does everything. He is very important for the team.
"Every game, he plays very well. He scored a beautiful goal against Manchester United [in the 1-1 draw at Old Trafford in October] - today again. It's a pleasure to play with him."