Suarez struck twice either side of goals from Neymar and captain Andres Iniesta as Barca humiliated their arch rivals with an imperious performance at the Bernabeu.
They surged six points clear at the top with 30 from 12 matches and ratcheted up the pressure on under-fire Real coach Rafa Benitez who had the luxury of fielding the trio of Ronaldo, Gareth Bale and Karim Benzema but to little effect.
Barca's dominance in the 231st meeting between the two teams, which prompted the angry Real fans to roundly whistle their own players and chant for president Florentino Perez to step down, was all the more remarkable considering coach Luis Enrique had started with a fit-again Lionel Messi on the bench.
The Argentina captain, who has been out for nearly two months with a knee injury, came on for Ivan Rakitic just before the hour and promptly sent Suarez clear to score the European champions' fourth.
An utterly dominant Barca could easily have added to their tally in the closing stages and Real's humiliation was complete when substitute Isco was shown a straight red card for a wild lunge at Neymar six minutes from time.
"We played what was quite honestly a complete match in every sense," Iniesta, who was given an ovation by the home fans when he was substituted late on, told Spanish television.
"There is a long way to go, it's not decisive at all but we are going away very, very satisfied," added the Spain playmaker.
A giant French flag was unfurled in the stands and the Marseillaise played during a minute's silence before kickoff to honour the victims of the Paris attacks and security was tight for the clash in the Spanish capital.
In an ominous sign for the home side, Barca had the first clear chance of the game when Suarez laid the ball off to Neymar in the seventh minute but the Brazil forward fired wildly over.
Sergi Roberto burst through the middle and played Suarez in on the right of the penalty area to open the scoring in the 11th minute with a clinical finish.
James Rodriguez had Real's only dangerous shot of the first half in the 28th minute before Iniesta slipped a pass through for Neymar to make it 2-0 five minutes before the break.
Marcelo had to clear a Suarez effort off the line moments before halftime after brilliant work from Neymar and as the players trooped off, a cacophony of whistles rang out around the stadium mixed with chants for Perez to go.
FULL BLAST
Real came out fighting after the break and Marcelo and Rodriguez each went close before Neymar sent a backheel into Iniesta's path in the 53rd minute and he hammered the ball past Keylor Navas into the top corner.
Isco came on for Rodriguez shortly after and initially gave Real some much-needed zip in attack, with Cristiano Ronaldo, Gareth Bale and Karim Benzema largely anonymous.
Suarez's second effort in the 74th minute was the 20th he and Neymar have scored between them out of Barca's last 21 goals in La Liga.
After the whistle, thousands of Real fans waved anything white they could get their hands on in the traditional sign of discontent with the board of directors while the music came on full blast to drown out any more embarrassing chants.
Chasing a sixth La Liga title in eight years, Barca have 30 points, with Real, who lost 3-2 at Sevilla in their previous outing, on 24.
Atletico Madrid can climb back to within four points of Barca and leapfrog Real into second with a win at promoted Real Betis on Sunday.
Valencia missed a chance to move above Celta Vigo into fourth when they lost the lead in a 1-1 draw at home to Las Palmas as Celta lost 2-0 at Galician rivals Deportivo La Coruna. Valencia have 19 points while Celta remain on 21.
Goals from Imanol Agirretxe and Xabi Prieto gave Real Sociedad coach Eusebio Sacristan a winning start in a 2-0 success at home to stuttering Sevilla.
(Additional reporting by Jesus Aguado, editing by Clare Fallon, Ken Ferris and Ian Chadband)
source: www.abs-cbnnews.com
