Hazard wore the Madrid jersey for the first time since his big-money move from Chelsea, while fellow recruits Luka Jovic, Ferland Mendy and Rodrygo Goes also made their bows for Zinedine Zidane's side.
But Corentin Tolisso, Robert Lewandowski and Serge Gnabry stole the show as Bayern put Madrid to the sword in the second half, which saw Zidane change his entire XI after the interval.
Tolisso opened the scoring in the 15th minute and Bayern completely dominated in the second half, with substitutes Lewandowski and Gnabry condemning Madrid to defeat in its ICC opener.
Madrid did have something to celebrate when Rodrygo capped his debut with a stunning 84th-minute free-kick after Sven Ulreich was sent off for bringing down the former Santos youngster.
Gareth Bale was left out of the Madrid squad amid ongoing uncertainty over his future, with the Welshman linked to Bayern. While there was no room for Bale, Jovic, Rodrygo and Mendy were on the bench.
It was an entertaining and end-to-end first half, with Bayern's Manuel Neuer the busier of the two goalkeepers at NRG Stadium.
After Neuer managed to make a goal-line save to deny Karim Benzema in the 11th minute, Bayern broke the deadlock four minutes later via Tolisso.
A low cross from Kingsley Coman found a way through to Tolisso, whose initial shot was stopped on the line by Thibaut Courtois, but the Frenchman made no mistake with the rebound.
Madrid huffed and puffed in search of an equaliser, with Benzema, who failed to capitalise on a pair of consecutive close-range chances, in the thick of the action but unable to put the ball over the line.
Sergio Ramos, Luka Modric and Hazard also had opportunities for Madrid prior to half-time, however, Bayern managed to preserve its advantage.
Madrid controlled possession early in the second half but Bayern was a threat in attack and the German giant sent a warning when an unmarked Thiago Alcantara drove into the box, however he was unable to direct Coman's cross on target approaching the hour mark.
That warning went unheeded as centre-back Niklas Sule picked out Lewandowski with a ball over Madrid's defence in the 67th minute and the Polish striker produced a stunning piece of skill to control it before turning and finishing into the bottom corner.
Gnabry completed the rout two minutes later when the German found himself unmarked in the area and he had time to take a touch and fire a half-volley past Keylor Navas.
Bayern ended the match with 10 men after Ulreich was red carded for a foul on Rodrygo outside the area in the 81st minute after Joshua Kimmich's sloppy back-pass and the Madrid signing converted his own free-kick to pull a goal back.