Jose Mourinho's Real drew first blood in the opening Clasico of the campaign when Karim Benzema punished a mistake by Barca goalkeeper Victor Valdes to score after 23 seconds.
A trademark weaving run from World Player of the Year Lionel Messi created Barca's equaliser for Alexis Sanchez after half-an-hour before Xavi's deflected strike on his 600th appearance for Barca made it 2-1 eight minutes into the second half.
Daniel Alves galloped down the right wing and sent over a deep cross for former Arsenal captain Fabregas to nod in Barca's third in the 66th minute.
Pep Guardiola's eighth victory in 12 Clasicos since he took the helm at the end of the 2007/08 season put his Barca side on 37 points from 16 matches, level with Real, who have a game in hand, but ahead on goal difference.
Real can restore their three-point lead with a win at Sevilla next weekend, as European champions Barca head to Japan for the Club World Cup.
Saturday's defeat ended Real's run of 10 straight league wins and prevented them from breaking the club record of 15 consecutive victories in all competitions.
"I think we were very superior to Madrid today, despite the mistake we made in the first minute," Barca playmaker Xavi said in an interview with Spanish television.
"We wanted to be brave here and we knew we could not win any other way," added the Spain international.
"The team produced a brilliant performance in all areas of the pitch and although we know there is a long way still to go we leave here on a high."
HOSTILE STADIUM
Several hundred million fans around the world tuned in to watch one of the biggest fixtures in club football, with Mourinho's Real out to prove there had been a shift in power in Spain and stretch their lead to six points with a game in hand.
However, Guardiola's side had prepared a different script and showed their mettle to battle back into the contest at a packed and hostile Bernabeu stadium.
In a match free of the mass brawls, sendings off and allegations of bias that marred recent meetings between the world's biggest-earning clubs, Barca exerted their customary domination of possession and could have added several goals to their tally in the closing stages.
Real's former World Player of the Year Cristiano Ronaldo, joint La Liga top scorer with Messi on 17 goals, had a frustrating night and missed several good chances, including a free header midway through the second half.
But it was Barca's night that got off to the worst possible start when Valdes's howler gifted Real a shock early lead.
The visiting goalkeeper's attempted pass went straight to Angel di Maria and the Argentine winger's cross eventually found its way to Benzema who volleyed in from close range.
Barca were level when Messi left several markers for dead and slipped the ball into space for Sanchez, who galloped through and sent a powerful low shot past Iker Casillas into the corner of the net.
