Despite missing Lionel Messi through injury, champions Barca started and ended in unstoppable fashion, while Real for long periods chased shadows under the burden of a winless run that now stretches to five games in La Liga.
Jordi Alba had already torn dangerously free down the left wing once when his cut-back found Philippe Coutinho unmarked 10 yards out, the Brazilian sweeping home the opener past the Thibaut Courtois and Sergio Ramos on the line.
It was a move that summed up the home side’s early dominance, and more was to come.
Suarez was clumsily brought down by Raphael Varane in the area, the referee awarding the penalty after consulting with the video assistant, and Lopetegui pounding the air furiously because play had initially been allowed to go on.
Real Madrid, winners of the past three Champions Leagues, were looking desperately short on confidence, but they emerged from the break transformed and almost dragged themselves level in a 10-minute spell of clear superiority.
First Marcelo poked home from close range after good work by Isco and substitute Lucas Vazquez down the right, before Gareth Bale clipped the inside of the post with a strike that left Marc-Andre ter Stegen relieved to see the ball ping out and back across his goal-line.
And Real again came close to drawing level when Karim Benzema missed with a header from a delightful Vazquez cross.
But when the next goal did arrive, it was Barca’s Suarez who found the net with a decisive, predatory header, the Uruguayan powerfully directing his second goal past Courtois from a standing start and stopping the Madrid revival in its tracks.
And the best was yet to come from Suarez. As the visitors crumbled at the back, Suarez ran clear. With only Courtois to beat to seal his treble, the former Liverpool striker dinked a wonderful chip over the ex-Chelsea keeper and across the line.
There was sheer, unbridled delight in the stands, where Messi, wrapped up against the autumn cold on and still recovering from his broken arm, would have more than approved.
But the loudest cheer of the night came as Arturo Vidal headed in a fifth goal in the closing stages, the final flourish to a scoreline that left Madrid’s players crestfallen as they trundled off the Nou Camp pitch, soundly beaten and fully aware of the reaction this result will bring.
They had begun the day within four points of Barca but now trail the leaders by seven and find themselves ninth in the table after 10 matches.