Real Madrid took the lead in the first half, when Chelsea goalkeeper Ann Katrin Berger offered Caroline Weir an open goal after a deft clearance to say the least.
After the break, Chelsea equalized on penalties – Guro Reiten placed the penalty kick on the post and the ball then went into the goal via Real Madrid goalkeeper Maria Rodriguez's back.
Chelsea pressed for a winning goal, which would have meant promotion, but failed to outsmart Rodriguez any further.
Johanna Rytting Kaneryd was substituted in the second half for Chelsea, while goalkeeper Zecira Musovic remained on the bench.
In Real Madrid, Freja Olsson sat on the bench for the entire match.
Two rounds remain in the group stage.
Chelsea top Group A, three points ahead of Paris SG.
Real Madrid are third, with two points up for a play-off spot