Entertainment right to the end
Schurrle, who missed the last four games for the hosts, came on just before the hour mark and grabbed an 87th-minute equaliser which was nothing more than what Thomas Tuchel's side deserved.
Cristiano Ronaldo started the scoring on the night before Pierre-Emerick Aubameyang scored the equaliser just before half-time.
Raphaël Varane restored the visitors lead midway through the second half but Schurrle's late strike meant that the points were shared as both teams went to four points from their opening two games in the group.
The hosts started the game at a blistering pace and despite Ronaldo's free-kick which was well saved by Roman Bürki at the other end, Keylor Navas saved the visitors from going behind on a couple of occasions early on.
Firstly he made a very good save to keep out a well-struck free-kick from Gonzalo Castro before keeping out a shot from Aubameyang.
Ronaldo netted opener against the run of play
As always though with the quality that Madrid have they can always hurt you on the break and that is what they did. Ronaldo was the scorer as he often is but the goal was made by a brilliant team move with it leading to a brilliant back-heel assist from Gareth Bale which was well weighted into Ronaldo's path and he smashed the ball home.
Dortmund though continued to press forward and they should have been level midway through the first half. Ousmane Dembele tricked his way into the Madrid box, finding some space, but instead of crossing the ball to his teammates, who were in a better position, he went for a curling shot which went over the bar.
As the half went on, the hosts started to become frustrated as it looked like they would go in at half-time 1-0 down. They didn't though as they got the equaliser their overall play deserved.
Aubameyang punished Navas' mistake to score equaliser
Raphaël Guerreiro took a free-kick from outside the box which Navas got too but punched the ball, when he should have got it to safety, straight to Aubameyang to put it into an empty net. It was a terrible error from the goalkeeper, who has only returned from injury after two months out.
It meant that score was level at half-time which was the least that the hosts deserved.
The hosts kept up their momentum at the start of the second half as Aubameyang and Dembele both went close to putting their side in front early in the second half.
Madrid though almost stole their way in front once again when a lovely cross from Sergio Ramos into the box found Ronaldo but he totally misjudged the ball and couldn't put his header into the net which was a big let-off for the hosts.
Varane put the visitors back in front
The visitors though did retake the lead midway through the second half. A brilliant cross from Ronaldo found Karim Benzema at the back post but the striker's shot came back off the post but Varane was there to tap the ball home into an empty net.
After the goal, the visitors sat deep waiting to counter attack on the hosts and they almost did it perfectly but Ronaldo spurned a big chance when he put his shot over the bar.
Schurrle's late strike ensured a share of the points
This gave the hosts hope as they started to pile the pressure on once again to get an equaliser. Despite Navas making two big saves beforehand, Dortmund managed to find the equaliser through substitute Schürrle.
Madrid failed to deal with a cross properly and the ball fell to the winger, who smashed the ball into the net with his left foot to give his side parity again.
This was to the be the last meaningful action in the game that the hosts dominated and fully deserved to at least get a point from.