Belgium were heading out of the World Cup in Russia after they found themselves two goals down to Japan shortly after the start of the second half.
The Japanese side matched Belgium and gave a good account of themselves in a breathtaking game.
Goals from Genki Haraguchi and Takashi Inui had fired Japan into a two goal lead shortly after the start of the second half.
But after a double change from Roberto Martinez, Jan Vertonghen headed Belgium a lifeline, with substitutes Marouane Fellaini and Nacer Chadli then completing the comeback.
Hazard set up Fellaini for the equaliser but he conceded Belgium were worried they were heading out of the tournament in similar circumstances to their shock quarter-final loss to Wales at Euro 2016.
“To be fair we were thinking two years ago against Wales,” Hazard told a news conference after the game. “But we were also thinking that we could score goals to win.
“We have players who can change the game, players on the pitch and from the bench can make the difference. Today we’re just happy to have won the game and to go on to the quarter-final.
“During the first 20 to 25 minutes of the first half, we were quite good. But what went wrong was at the beginning of the second half – this is where we conceded two goals. And those two goals were avoidable.
“We had some little defensive errors but the reaction we showed tonight was great. Maybe we needed this type of match for the future. We could have been eliminated, but we ended up in the quarter-finals. So we’re all very happy.”