Vinicius Junior opened the scoring just before the break as Carlo Ancelotti's side mounted a spectacular comeback from their one-goal semi-final first leg deficit, with Benzema adding a second-half treble.
After netting three at the weekend against Real Valladolid in La Liga, Benzema repeated the trick to humiliate Barcelona on a painful night for coach Xavi Hernandez in front of almost 95,000 distraught fans.
Los Blancos trail their arch-rivals by 12 points in La Liga and were beaten by Barca in the Spanish Super Cup final in January, but triumphed here to reach the Copa final for the first time since 2014, where they will face Osasuna.
"It was a complete game - when you play a complete game, you win 4-0 like that," said Ancelotti.
"This is the most important moment of the season and when we're at the right temperature (like this), we're good."
Barcelona's Sergi Roberto said letting in Vinicius' goal on the stroke of half-time was a huge blow.
"Their goal at the end of the first half killed us, we didn't deserve to let in that goal. I think we were better in the first half," the midfielder told RTVE.
"We created more chances that we didn't put away, and that goal hurt our morale. In the second half they scored the second and we couldn't play our game."
The Catalan said defeat would not damage Barcelona's title bid in the final weeks of the season.
"Now we have a considerable points distance, it will not affect us, we have to continue and go for the league," he added.
"Congratulations to Real Madrid, they had a great second half and compete very well," said Xavi.
"If you let Madrid off the hook, they don't forgive you. It's not by chance they have won the Champions League - they have a great team."
Madrid have lifted the Copa del Rey on 19 occasions, while their opponents Osasuna have never won it, securing passage to their second final after beating Athletic Bilbao on Tuesday.
