The hosts threatened a major upset by giving the current holders a real scare in the first half, although they entered the break showing nothing for it.
This proved costly, as Real found their advantage unforgiving. Vinicius Junior and Luka Modric struck back-to-back, before Hazard netted a sublime team goal to cap off the evening in style for Carlo Ancelotti’s side.
Prior to this clinical display, Celtic enjoyed a very positive opening for the first 45 minutes. Liel Abada couldn’t take a few presentable opportunities, while Callum McGregor saw his effort cannon fall back from the woodwork.
The visitors’ problems escalated when Karim Benzema was sent off with an injury after just 30 minutes.
Real stepped up after the break and a ruthless four-minute spell gave them full control of proceedings at Celtic Park.
Federico Valverde stepped forward on the right wing, launched a perfect low cross into the box and Vinicius was there at the back post to run over it, guiding a fine finish into the far corner.
Celtic barely had time to collect their thoughts before the lead was doubled. Real broke numbers as Luka Modric charged into the box, kept the ball under control as he cut inside and finished with the outside of his foot which proved too good for Joe Hart.
A long spell of sustained possession brought the third goal, as Toni Kroos quickly upped the ante with a fine pass over the top for Dani Carvajal. He squared it off the volley into the path of Hazard, who couldn’t miss from inside the penalty area.