Despite the draw, Madrid stay top of the group on seven points same point as Tottenham but ahead on superior goals advantage.
At the Etihad Stadium, Manchester City edged in form Napoli 2-1 to make it three straight wins in Group F.
Early goals from Raheem Sterling and Gabriel Jesus in the ninth and 13th minutes respectively put City 2-0 up.
Napoli had a chance to get back into the game but Dries Mertens missed a 38th minute penalty.
Napoli eventually pulled a goal back with Amadou Diawara from the penalty spot on 73 minutes but City held on to claim all three points.
City sit top of the group on nine points, while Napoli drop to third on three points.
In Group E, Liverpool secured their first win following a commanding 7-0 away win against Maribor, the biggest ever away win for an English side in the Champions League.
A brace from Mohamed Salah (19th, 40th minutes) and Roberto Firmino (fourth, 54th minutes) and a goal each from Philippe Coutinho (13th minute) Alex Oxlade-Chamberlain ( 86th minute) and Trent Alexander-Arnold (90th minute) sealed the massive win for Liverpool.
The win saw Liverpool go top of the group on five points.
In other results, Dortmund got their first point in Group H following their 1-1 away draw against Apoel Nicosia, Shakhtar Donetsk beat Feyernoord 2-1 away, AS Monaco were stunned 2-1 at home by Besiktas, RB Leipzig edged visiting FC Porto 3-2 and Sevilla were spanked 5-1 by Spartak Moscow in Russia.
2017/2018 UCL matchday 3 results:
Real Madrid 1vs 1Spurs
Apoel Nicosia 1vs 1 Dortmund
Man City 2 vs 1 Napoli
Feyenoord 1 vs 2 Shakhtar Donetsk
AS Monaco 1 vs 2 Besiktas
RB Leipzig 3 vs 2 FC Porto
Maribor 0 vs 7 Liverpool
Spartak Moscow 5 vs 1 Sevilla