The Chelsea ace is now almost certain to start Friday evening's quarter-final against Brazil, which Martinez hopes will provide one of his key men with the platform to further showcase his brilliance.
"He's been a real captain, a real leader and someone who's always been himself," he told reporters at his pre-match press conference. "What you love about his temperament is that whatever the score, opponent, moment, he's always available to get the ball and be decisive.
"His level of the play has been the highest, he's been decisive in attack, a leader in what the group needs to achieve. We are a team and in international football that [being a team] is difficult. He's played a massive part as captain of this group.
"You see a lot of the captain through the team. When you see Hazard enjoying his football, he makes it a beautiful sport, he puts a smile on the face."
Hazard is said to have been offered to Real Madrid by Chelsea earlier this summer after delaying contract talks.