Elsewhere, Leicester City topped Porto 1-0 to maintain a perfect record in their Champions League debut here on Tuesday, reports Efe.
Real Madrid took the lead in the 17th minute at Dortmund's Signal Iduna Park on a goal by star striker Cristiano Ronaldo. But the hosts pulled level just before half-time, when Pierre-Emerick Aubameyang exploited a poor clearance by Real goalkeeper Keylor Navas.
Defender Raphael Varane put the defending champions up 2-1 with a goal in the 68th minute and the visitors seemed on the verge of a victory until German international Andre Schurrle equalised for Dortmund with a spectacular strike in the 87th minute.
The outcome leaves the sides tied for first place in Group F with four points each, one ahead of Potugal's Sporting Lisbon, who beat last place Poland's Legia Warszawa 2-0 also on Tuesday.
Juventus, held 0-0 in Turin by Sevilla in their Champions opener, trounced Croatia's Dinamo Zagreb 4-0 in Zagreb thanks to goals in the first half by Miralem Pjanic and Gonzalo Higuain, a second-half marker by Paulo Dybala and a Dinamo own goal.
The win brings the Italian club to four points, tied at the top of Group H with Spain's Sevilla, 1-0 victors at home over Olympique Lyon on a goal in the 53rd minute from Wissam Ben Yedder.
Tottenham defeated CSKA Moscow of Russia on a goal in the 71st minute by Son Heung-Min.
France's Monaco drew 1-1 at home against Bayer Leverkusen of Germany and lead Group E with four points.
Leicester, despite struggling to defend their English Premier League crown, defeated visiting Porto 1-0 with a goal from Islam Slimani to take a solid lead in Group G.
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