Barcelona had moved two points clear with a 3-1 success at Getafe, Lionel Messi, David Villa and Pedro netting for the champions, before Jose Mourinho's Real snuffed out Atletico's bid for a first Madrid derby win in more than a decade.
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Real have 26 points from 10 games, Barca are second on 25 and Villarreal, who fought back from a goal down at home to beat Athletic Bilbao 4-1, third on 23.
Espanyol are in fourth after their 1-0 win over visiting Malaga on Saturday and Valencia can move above them with a win at Sevilla on Monday.
The Madrid derby was potentially Real's first genuine test of the season after they had swatted aside mostly mid- to lower-table opposition in their previous matches of the campaign.
However, Atletico strikers Diego Forlan and Sergio Aguero saw too little of the ball and wingers Jose Antonio Reyes and Simao threatened only rarely down the flanks.
After his Portugal defensive partner Pepe had gone close with a header at a packed Bernabeu stadium, Carvalho burst through from the back to fire Real ahead in the 13th minute.
German international Ozil, a firm favourite with the Real faithful following his move from Werder Bremen, then bamboozled Atletico goalkeeper David De Gea with a low, swerving free-kick from wide on the right to make it 2-0.
Toothless Atletico's best effort of the first half came in the 36th minute when former Real and Arsenal winger Jose Antonio Reyes forced a fine save from Iker Casillas with a curled shot.
Real striker Gonzalo Higuain and Forlan hit the woodwork with superb volleys in the second half but Atletico never looked like getting back into the match.
RICH VEIN
Portuguese Mourinho said he had instructed his players to slow down the pace of the game to allow them to control it more easily and nullify Atletico's attacking threat.
"My players were very good and if we did not put on more of a spectacle it was because of our opponent and not us," he told a news conference. "You can't beat a team like Atletico by six or seven."
World Player of the Year Messi continued his rich vein of scoring form by taking his tally for the season to eight, three behind Real's Cristiano Ronaldo.
Getafe crowded their own half but Barca weaved an intricate web of passes to set up Messi after 23 minutes and the Argentine scored inside the near post.
His subtle layoff created the second for Villa and Pedro grabbed the third after Barca pressured the home defence into a mistake in the 65th minute.
