Neymar gave Barcelona a fourth-minute lead to silence the Santiago Bernabeu but Real tore after La Liga's leaders in search of a response.
It arrived from the penalty spot 10 minutes before half-time, Cristiano Ronaldo coolly converting after Gerard Pique handled Marcelo's cutback.
Pepe and Karim Benzema netted in a high-octane opening to the second period to close out a deserved triumph on the back of Wednesday's dominant 3-0 UEFA Champions League victory at Liverpool.
Reflecting on how Real overcame their bitterest rivals, Ancelotti told reporters: "The best thing? The effort. We didn't lose our head after we conceded.
"We continued with our ideas and everything worked out. There was a lot I liked about the team. The tempo was high and we recovered well from Wednesday.
"I've always thought defending wasn't a question of quality but one of sacrifice. I run a serious and professional team who know what it is to play for Madrid and to sacrifice.
"We wanted to attack with possession, using the wings. In the second half we won because we wanted to win."
Ancelotti reserved particular praise for Isco, who has made the most of the starting berth handed to him by Gareth Bale's injury absence this week.
"Isco's work was fantastic but to beat Barca we need everyone to work," said Ancelotti, after the Spain international drove forward the superb counter-attack from which Benzema struck the decisive 61st-minute third goal.
"Everyone was to a very high standard and it wasn't easy after only two days of rest since the Liverpool game.
"Bale is central to this team and he'll play, but it's good for the team that I don't only have 11 players.”
And Ancelotti believes the mental strength in evidence throughout his stellar squad bodes well for the season ahead.
"We showed against Liverpool and here that the physical side isn't everything. We're also mentally convinced we're doing well," he said.
"I talk about concentration, thinking about what we're doing, to follow the strategy and the instructions.
"It's hard to compare with other teams but I think this is a serious squad."
Real are now a solitary point behind Barcelona after handing their old foes a first league loss of the campaign.
Ancelotti added: "This is an important win because the opponent was very strong and we reached our goal of cutting the points gap. That's why we’re all satisfied."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
