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It is the second consecutive away game which Barca failed to win after losing 1-0 at Athletic Bilbao two weeks ago.
The result means Atletico Madrid are the only team left in La Liga to have won all of their games this season, with Diego Simeone's side hosting Eibar on Sunday.
The 38-year-old came off the bench late in the game and soon made Barca pay for squandering several chances by acrobatically lashing an unstoppable shot into the net in the 89th minute.
Luka Modric was dismissed 11 minutes into the second half, but Lucas Vazquez extended Real's lead with 10 minutes of the match remaining.
Karim Benzema looked to have fired Madrid to a second straight win after last week's confidence-boosting 3-1 victory at Celta Vigo when he scored in the 82nd minute with a splendid piece of skill.
LaLiga Football Schools, a grassroots development initiative by the Spanish football league, along with India On Track will be providing comprehensive training to Indian children and coaches.
It was an utterly dominant performance from the La Liga leaders which avenged their 4-3 loss at home to Betis in November and took them on to 66 points after 28 games.
Lionel Messi and Luis Suarez were largely kept quiet in a shy display from the champions in which their defenders Gerard Pique and Clement Lenglet were the heroes instead, bravely putting their bodies in the way to snuff out Madrid.
Results 191-198
