The Brazilian opened the scoring at Camp Nou before his Chilean team-mate doubled the home side's advantage with a stunning goal shortly after coming on as a substitute during the second half.
Neymar played his part, having released Alexis into space, but he was reluctant to take any credit for what was a sensational finish.
"I'm lost for words," Neymar told reporters. "It's a golazo."
The 21-year-old did admit, though, that he had thoroughly enjoyed what was his first taste of the biggest fixture in world football, arguing that while he had been impressed with Cristiano Ronaldo's performance, he felt that Barca were good value for their win.
"It was very emotional to score in a the game in which all players want to play," Neymar enthused. "I'm very happy about such a special goal but above all for the three points we got.
"I had seen many Clasicos, so it was great to play one. But it was so hard against a great team. Cristiano [Ronaldo] is a great player, but we have also many good players.
"I'm so happy about the victory, the team and the goal."
Meanwhile, Neymar's team-mate Alexis was ecstatic after effectively deciding the game in Barcelona's favour with his moment of magic.
"I'm very happy about the goal and the match. I saw Diego Lopez had advanced too much so I tried to hit the ball over him," the Chilean said.
"This is a very beautiful match that everybody wants to play. Real Madrid is a very hard team to beat, it was not easy."
The Spanish champions now sit six points ahead of third-placed Madrid in la Liga.