Zinedine Zidane’s side was poor again at the Bernabeu and was almost undone by two bizarre goals from 21-year-old Emmanuel Dennis.
The Nigerian’s first came as he miscontrolled Percy Tau’s cross past a wrong footed Thibaut Courtois and into the net initially disallowed for offside but awarded after a long video assistant referee delay.
For the second, Dennis stumbled into the box and chipped Courtois who was replaced by Alphonse Areola at half-time despite almost losing his footing.
Captain Sergio Ramos responded for Real in the second half with a header from Karim Benzema’s cross, which was ruled out for offside but overturned by the VAR.
After Bruges captain Ruud Vormer was sent off for two bookings, Toni Kroos crossed for Casemiro to head in the equaliser from the resulting free-kick.
Real beaten 3-0 by Paris St-Germain in their opening game remains bottom of Group A.