But beyond this, it was a game which surely will signal the end of hapless coach Julen Lopetegui’s spell in charge of Real Madrid.
Barca’s Philippe Coutinho opened the scoring in the 11th minute following a slick team move.
Suarez doubled their advantage on the half-hour mark by converting a penalty kick awarded after consultation with the video assistant referee (VAR).
Real had looked lifeless in the first half but produced a courageous display after the break following a tactical switch from Lopetegui.
They deservedly pulled a goal back through Marcelo and came close to grabbing an equaliser as Luka Modric struck the post and Sergio Ramos headed narrowly over.
Yet even without their injured talisman Lionel Messi, Barca soon reasserted their authority and ran riot in the final 15 minutes with two more goals from Suarez.
A header from substitute Arturo Vidal further twisted the knife into Real, who have lost their last three league games.
They are now seven points behind Barca in the La Liga standings in ninth position.
“This result is a reflection of our entire season, which has been a disaster,” Real midfielder Casemiro later told reporters.
“It’s not about tactics or attitude, it’s everything. The players have to run more and fight more. We aren’t playing well and we can’t blame the coach, as the players are the ones who have to perform on the pitch.”
Real looked to be lacking in confidence from the start as Benzema hurriedly hammered a cross from Gareth Bale over the bar when he had plenty of time to bring the ball under control.
Barca, meanwhile, oozed belief and their opening goal was a joy to behold as Ivan Rakitic released Jordi Alba with a chipped pass.
The Spaniard rocketed past Nacho, crossing freely into the area for Coutinho to turn the ball in from close range.
Further signs of Real’s nervousness came when Nacho misplaced a pass in the area to the feet of Arthur Melo.
It took a magnificent flying save from Thibaut Courtois to beat away the Brazilian’s curling shot.
Barca did extend their advantage when Suarez slammed a spot-kick under the diving Courtois.
This was after he was tripped by Varane, who was responsible for both goals Real conceded in their shock 2-1 home defeat by Levante last week.
Lopetegui rejigged his formation at the start of the second half, opting for a back-three by hauling off Varane for Lucas Vazquez.
His side instantly improved, getting a foothold through Marcelo’s strike, and moments later they were agonisingly close to finding an equaliser.
But Barca continued to look dangerous on the break and Suarez’s bullet header from a standing position killed the game off as a contest.
“We had 15 difficult minutes but we had a great performance,” said Barca coach Ernesto Valverde.
“The first half belonged to us. They turned things around by playing fullbacks as wingers and we were caught out by it and suffered after their goal.
“Then we sorted ourselves out and took advantage of their risky approach.”
Uruguay striker Suarez completed his treble with a classy chipped finish while Chile international Vidal struck his first goal for Barca to further humiliate Real Madrid.
They were condemned to their worst defeat in a ‘Clasico’ since a Barca side coached by Pep Guardiola beat them 5-0 in 2010.