Second-half goals from Luis Suarez, Lionel Messi and Aleix Vidal ensured another memorable Clasico victory for Barcelona as they recorded a third successive La Liga win at the home of their fiercest rivals for the first time in their history.
The victory also takes Barcelona nine points clear at the top of the table and a full 14 above defending champions Real Madrid, whose title defence appears to be in tatters heading into the winter break.
The hosts - who were returning to domestic action following their Club World Cup triumph in Abu Dhabi - had the ball in the back of the net inside just two minutes when Casemiro's flick from a corner was nodded in off the underside of the crossbar by Cristiano Ronaldo, but the celebrations were cut short by the linesman's flag.
Real Madrid looked the most likely to break the deadlock in the opening exchanges, though, and Ronaldo squandered a clear chance after 10 minutes when the reigning world player of the year completely missed the ball after being teed up inside the area.
It took until the half-hour mark for Barcelona to register their first shot of the contest, but it was one which drew a smart save from Keylor Navas as Paulinho latched on to a fine Messi pass before seeing his powerful first-time half-volley tipped over the crossbar.
Ronaldo continued to look the most likely for the home side, and he almost turned creator moments later with a low ball into the box which required an important interception from Gerard Pique to thwart Karim Benzema.
Messi was largely kept quiet in the first half, but he did burst into life to create another chance for Paulinho six minutes before the interval as the Brazilian got in front of his marker to meet Messi's cross, drawing another save from Navas.
It was Madrid who came closest to breaking the deadlock in the opening 45 minutes, though, with Benzema clipping the outside of the post with a glancing header having been picked out by Marcelo's delivery.
The two sides went into the break all square, though, and it was Barcelona who came out stronger in the second half with Suarez drawing an early stop from Navas following good work from Jordi Alba down the left flank.
Suarez did have his goal just one minute later when he put the finishing touch to a devastating team move, with Sergio Busquets, Ivan Rakitic and Sergi Roberto all involved before the Uruguayan swept the ball under Navas from inside the penalty area.
Suarez then crashed an effort into the side-netting before Paulinho drew another save from Navas as the visitors looked to increase their advantage over their bitter rivals.
The second goal arrived shortly past the hour mark, but only after a flurry of activity inside the Real Madrid box; Suarez was first denied when one on one with Navas before hitting the post from the rebound, and Pique then saw another follow-up effort kept up by Dani Carvajal's deliberate handball.
Barca did eventually smuggle the ball over the line, but referee Jose Sanchez called play back for the handball and was left with no other option but to show Carvajal a straight red card.
Messi stepped up to the resultant spot kick and slammed it into the roof of the net for his 25th El Clasico goal, setting his side well on course for an unprecedented third consecutive La Liga win at the Bernabeu.
Barcelona were in no mood for mercy against the defending champions, though, and Navas was called into action once again with 20 minutes remaining when he kept out Messi's low effort.
Zinedine Zidane did finally react to going two behind when he brought on Marco Asensio and Gareth Bale, and the latter should have given the hosts a lifeline with 12 minutes remaining when he could only put a clear chance straight at Ter Stegen.
Ter Stegen denied Bale again moments later, but Madrid's desperation to pull a goal back and breathe new life into the title race left space in defence which Nelson Semedo nearly exploited 10 minutes from time, only to be denied by Navas.
Madrid were soon back on the front foot, though, and Sergio Ramos almost restored his side's hope with a powerful strike from a tight angle which Ter Stegen bravely saved from close range.
The hosts realistically needed one of those chances to go in if they were to drag themselves back into the match, and it was Barcelona who threatened a third in the closing stages as first Messi and then Andre Gomes came close.
Ernesto Valverde's side did rub salt into the wound with virtually the last action of the match when Messi laid the ball back for Vidal, whose shot had enough on it to squirm under Navas and creep over the line just minutes after his introduction.
The goal put the seal on an historic victory for Barcelona, and also one which holds huge significance in the present day as they moved 14 points clear of the newly-crowned Club World Cup champions.
Madrid do still have a game in hand over the teams above them in the table, but they could end the weekend as low as fifth following their third defeat of the season, whereas Barcelona remain unbeaten in La Liga.
Real Madrid (4-4-2): Navas; Carvajal, Varane, Ramos, Marcelo; Modric, Casemiro (Asensio, 72'), Kovacic (Bale, 72'), Kroos; Ronaldo, Benzema (Nacho, 66')
Barcelona (4-4-2): Ter Stegen; Roberto (Vidal, 91'), Pique, Vermaelen, Alba; Paulinho (Gomes, 84'), Rakitic, Busquets, Iniesta (Semedo, 77'); Messi, Suarez