Luis Suarez scored twice with Neymar and Andres Iniesta getting the other goals in a 4-0 win for Barca while Real were unable to cause many problems for the visitors' backline.
Bravo, who has now not conceded in his last three league games, did though make several telling saves when called on, including two one-on-ones with Cristiano Ronaldo.
“We have dynamite in attack but along with that we have players that build play and we are very solid at the back,” Bravo told reporters.
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“When you face a team like Madrid then you know that they are going to attack you in your own half but we remained calm defensively and did our work well. They had some shots and I was able to make the saves.”
The win helped Barca open up a significant six-point lead over Real at the top of La Liga with 12 games played.
“We always go out to play our own game and keep possession. This doesn't change depending on the rival. It was an incredible game and we are looking very solid at the moment,” said Bravo.
“Part of the idea of keeping hold of possession is that you also frustrate the opposition and this obviously reduces their chances of scoring as well. This is how we play and it worked out perfectly.”
Victor Valdes was Barca's keeper during a golden period for the club when they won three Champions Leagues and six La Liga titles between 2004 and 2013.
Bravo, however, was quick to prove himself after the loss of such an iconic figure in 2014 and played assuredly as they won the treble in his first campaign.
He suffered a calf injury in September which coincided with a lapse in form by Barca with the less experienced Marc-Andre ter Stegen taking his place.
His return, however, prompted a resurgence and the Catalan side are now showing the ominous form that brought them success last season.
(Reporting by Tim Hanlon in Barcelona, editing by Toby Davis)
