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 equalizer 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." Several hundred million fans around the world tuned in to watch one of the biggest fixtures in club soccer, 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.
Xavi's volley from just outside the penalty area struck Real defender Marcelo and looped onto a post and into the net and, after Fabregas's stunning effort, Messi, Andres Iniesta and Xavi all went close to scoring a fourth.
In the earlier kickoffs, Valencia ended a miserable week with another setback when they conceded twice in stoppage time to lose 2-1 at La Liga strugglers Real Betis.
Eliminated from the Champions League at Chelsea on Tuesday, Valencia were closing in on a morale-boosting win after Jose Antonio Dorado turned the ball into his own net midway through the second half before striker Ruben Castro bundled in for a 91st-minute equalizer.
The Canary Islander grabbed a dramatic second in the fourth minute of added time when he controlled the ball on his chest and lashed a shot high into the net past Diego Alves, sending the home supporters into raptures on a wet night in Seville.
Promoted back to the top flight at the end of last season, Betis had taken just one point from their previous 10 matches and Saturday's victory lifted them to 13th on 16 points from 15 matches. Valencia stay third, seven behind Barca and Real.
Surprise packages Levante strengthened their hold on Spain's fourth Champions League qualification berth when they beat fifth-placed Sevilla 1-0.
Defender Nano was quick to react when the ball broke loose at a corner in the 56th minute at Levante's Ciutat de Valencia stadium and he lashed it high into the net to lift Levante to 29 points from 15 matches, five ahead of Sevilla and one behind their more illustrious city neighbors Valencia.
