Watch every match of UEFA EURO 2016 live on beIN SPORTS
Toby Alderweireld's early header had opened the scoring and Yannick Ferreira Carrasco sealed the win with a stoppage-time goal after Hazard had made his mark.
Hazard created a total of four chances for his team-mates and was a constant threat down the left as Belgium produced what he felt was close to a perfect display to book a quarter-final against Wales in Lille – the city where he used to play – on Saturday (AEST).
Asked if this was his best Belgium performance, Hazard told reporters. "Yes. I had a lot of desire to win.
"We scored goals, created chances and Thibaut Courtois got his clean sheet so it was a good evening.
"Maybe it was not the best opponent but they were still a tough side to play against. It will be hard to improve on the performance as it was almost perfect. We played well.
"I knew they were a team with a lot of quality who defended well. I knew we would have to be patient to score a goal. My younger brother [Kylian, who plays in Hungary] spoke about that, we got some information and studied them."
Hazard is expecting a tough challenge against Wales, as Belgium took four points from the Dragons in two games during EURO 2016 qualifying.
"We are lucky enough to play in Lille. I know the city very well - if not the stadium as I didn't play there - so I will be very proud.
"Wales are a tricky side to play against, we met them in the qualification games. We didn't have many chances, they have a very compact unit and a great player up front. We will study them well."
