It is a first point for Real in Group A, which is led by PSG.
Paris: In Madrid, record 13-time champions Real were 2-0 down at half-time at home to Club Brugge, for whom the Nigerian forward Emmanuel Dennis scored a first-half brace.
But Zinedine Zidane's team came storming back as Sergio Ramos headed in before Casemiro claimed a dramatic equaliser in the 85th minute, seconds after Ruud Vormer had been sent off for the visitors.
It is a first point for Real in Group A, which is led by PSG. The French club, again missing the suspended Neymar, beat Galatasaray 1-0 in Istanbul thanks to Mauro Icardi's second-half goal.