South Africa international Tau was handed a return to the starting XI after missing his side's opener in the tournament against Galatasaray. He delivered an impressive showing along with Nigerian forward Dennis.
Tau set up the Nigeria U23 star's goal in the ninth minute, with the effort initially cancelled for offside before Video Assistant Referee (VAR) later allowed the goal to stand.
Dennis then scored his second goal in the encounter 30 minutes later as the Belgian team headed into the half-time break with a 2-0 lead.
After the restart, Zinedine Zidane’s men launched a comeback with Sergio Ramos reducing the deficit after receiving a pass from Karim Benzema.
Club Brugge were then reduced to 10 men after Ruud Vormer received his second yellow card in the game and was subsequently sent off.
Real capitalised on the misfortune of their visitors with Casemiro levelling proceedings with a header from the freekick.
Dennis, who has now scored five goals this season was replaced in the 71st while Tau made way for Schrijvers.
The draw saw Club Brugge climb to second spot in the Group A standings with two points from two games behind leaders Paris Saint-Germain.
The African stars will hope to maintain their fine performances for the Blue and Black in their next league game against Gent on October 6.