Cristiano Ronaldo scored the first goal of the night, giving his team the advantage after only 17 minutes.
Teenage duo Christian Pulisic and Emre Mor had chances to equalise in the last 10 minutes but Schurrle, who came on after 58 minutes, levelled late on.
87′ GOAL! Schurrle levels for Dortmund with a great strike.
Their 2-0 defeat at Dortmund in the 2014 quarter-finals did not prevent them from winning the tie on aggregate but it came a year after their 4-1 thumping in the first leg of the 2013 semi-finals, when Robert Lewandowski scored all four goals for Borussia.
Ronaldo sulked on Saturday after being substituted by coach Zinedine Zidane during a Spanish league match.
Real Madrid coach Zinedine Zidane has played down reports of a dressing-room spat between himself and Cristiano Ronaldo.
The home side, which had never lost to Real on German soil, responded with Aubameyang striking an effort against the crossbar with a fine effort.
At the other end, Gonzalo Castro s well-struck shot tested Costa Rica goalkeeper Keylor Navas, who was making his first appearance of the season after injury.
The second half brought yet more end-to-end football with both teams creating opportunities.
But Real took the lead when Ronaldo finished off a sweeping move. The ball hit Varane and bounced toward the net, with Aubameyang pouncing to score from close range.
Tuchel, whose side beat Legia Warsaw 6-0 in their group opener, added: “We need the same courage we show in a Bundesliga match or at Warsaw, and the same conviction and the same freedom to play situations as they come”.
Leicester City forgot their domestic struggles to secure a second successive Champions League victory as Islam Slimani tormented a familiar foe by grabbing the only goal in a 1-0 win over Porto on Tuesday. I took the decision for the good of the player. They’ve already beaten domestic rivals PSG 3-1 in Ligue 1 which followed a 4-0 loss against a Mario Balotelli inspired Nice last week, who have been in breath taking form since joining the French club after leaving Liverpool on a free transfer.
In Group E, Tottenham claimed a vital 1-0 win over CSKA in Moscow.
Mauricio Pochettino’s side were without Harry Kane, Mousa Dembele, Eric Dier, Danny Rose and Moussa Sissoko against the Russian champions but the in-form Son Heung-min was there and he made the difference.