The European champions beat Malaga 2-1 at La Rosaleda on Saturday to extend their winning run to 16 matches in all competitions, creating a new club record in the process.
Real had twice before won 15 in a row before being halted and, although Isco's late red card was followed by a stoppage-time goal by Roque Santa Cruz, the visitors did enough to earn victory.
Karim Benzema put Real ahead in the first half after good work by Cristiano Ronaldo down the left and the Portugal star was decisive again as they doubled their lead in the second period.
The Ballon d'Or frontrunner flicked on a lofted ball for Gareth Bale and the Welsh winger slammed home, the goal ultimately proving enough to clinch the record which has delighted Ancelotti.
He told reporters: "I'm happy. It feels like a dream. We're very happy about the run. I hope it continues.
"I'll get the credit for this, but I've been lucky to coach a fantastic team with fantastic players for a fantastic club.
"My admiration goes to the players, but this is only a small part of a long season.
"We must keep on working hard because in football, whatever happened is in the past. We all know this."
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