A Sergio Ramos brace established a comfortable cushion for Madrid in the first leg and Benzema capitalised with two first-half strikes at Estadi Montilivi in Thursday's return.
The former France international has now hit five goals in his last three appearances as he continues to thrive under the leadership of Madrid coach Santiago Solari.
Pedro Porro's strike proved only a consolation as Marcos Llorente wrapped up the scoring - meaning Madrid join Real Betis, Valencia and holders Barcelona in the draw for the last four of the competition.
Girona needed a fast start and they hit the woodwork in the second minute, Alex Granell's inswinging free-kick from wide on the right wing crashing back off the crossbar.
But Madrid took the lead in the 27th minute, Benzema swapping passes with Dani Carvajal to create space before thrashing a swerving drive past goalkeeper Gorka Iraizoz.
And Benzema put the tie beyond Girona before half-time, curling a wonderful strike beyond Iraizoz and in off the far post after linking up with Vinicius Junior.
Madrid should have added a third but when Iraizoz made a good save from substitute Marco Asensio, Lucas Vazquez somehow managed to hit the post with the goal gaping.
And while Porro beat Keylor Navas in the 71st minute to briefly spark hope for Girona, they had left themselves far too much to do and Llorente's fine run and 20-yard drive settled matters.
What does it mean? Benzema flourishing as Asensio and Bale return
Injuries to Asensio and Gareth Bale have left Benzema as the main man for Madrid and he has shone in the spotlight. Both Asensio and Bale are back now, but with Vinicius impressing again Solari now has decisions to make over the shape of his attack.
Benzema earns his rest
Striker Benzema was always the lowest profile member of the famous 'BBC' Madrid forward line comprising of himself, Bale and the departed Cristiano Ronaldo. But Benzema is on his hottest streak of scoring form for some time, and it was no surprise Solari took the chance to rest him early in the second half, bringing on the fit-again Asensio in his place.
Iraizoz caught out of position
Benzema's first goal was a vicious strike, but when he sees replays Iraizoz may feel he should have done better. The Girona goalkeeper took a step the wrong way, giving himself no chance of stopping the attempt.
Madrid's momentum will be threatened by Sunday's visit of high-flying Deportivo Alaves in LaLiga. After facing Madrid twice - plus league leaders Barcelona - over the last week, Girona will hope a trip to Eibar is less testing.