Diego Simeone's men would have fallen 10 points behind Real with defeat at the Vicente Calderon, but the Liga pacesetters were rolled over in ruthless fashion by a rampant Atletico side.
Victory extends Atletico's unbeaten run against their neighbours to six games this season, Real having been out-fought and out-thought as they failed to display the performance expected of a side at the top of the table.
Ancelotti, who insisted his men were "not scared" of Atletico, was able to call upon the services of Cristiano Ronaldo again following his suspension, but the visitors looked in trouble from the off and Tiago opened the scoring with 14 minutes gone.
Saul, an early substitute for the injured Koke, doubled their tally with a delightful bicycle kick four minutes later, leaving Real completely stunned.
The visitors rarely looked capable of mounting a response and Atletico added further goals through Antoine Griezmann and Mario Mandzukic to move within four points of Real at the summit.
Atletico began the contest with purpose and looked particularly threatening down the right flank through Arda Turan, who caused problems inside the first 10 minutes.
The hosts were dealt the blow of losing Koke to a hamstring injury in the 10th minute, but produced a marvellous response to the setback, taking the lead four minutes later.
In truth, there was a hint of fortune about the goal, as Tiago met Mandzukic's well-weighted pass on the edge of the area and drilled a low effort at Iker Casillas, who allowed the ball to squirm under him.
There was no doubt over the quality of Atletico's second, which came in the 18th minute.
Guilherme Siqueira produced a marauding run on the left wing, riding two challenges on his way, and then picked out a precise cross for Saul, whose acrobatic overhead kick flew in off the post.
Real picked things up after the half-hour mark, but Atletico continued to look lethal in attack and should have been awarded a penalty in the 34th minute when Sami Khedira blocked Diego Godin's goal-bound effort with his arm.
Atletico started the second half strongly and Griezmann tested Casillas with a stinging drive from the edge of the area, before sending a bicycle kick just over the crossbar.
The lively France star was not to be denied in the 67th minute, though, as Griezmann latched on to Saul's header across goal and poked in ahead of the sluggish Raphael Varane.
Real made a laboured attempt to salvage a consolation towards the end, but Atletico ultimately sapped them of their remaining pride as Mandzukic headed in substitute Fernando Torres' cross for a fourth, handing Simeone's side and second-placed Barcelona – who face Athletic Bilbao on Sunday – a huge boost in the title race.
