Benzema was on target in the first leg too, a 4-2 victory at the Santiago Bernabeu last week, and he continued his brilliant burst of form with another pair at Montilivi.
Pedro Porro pulled one back for Girona but any hopes of a comeback were extinguished when Marcos Llorente drove in for a 7-3 win on aggregate.
Madrid join Barcelona, Real Betis and Valencia in the draw for the last four on Friday.
Barca, who are chasing a record fifth cup success in a row, will be the ones to avoid but Santiago Solari’s team are gaining momentum, having won six out of their last seven games, with the resumption of the Champions League just around the corner. Start forecasting your weekend games Now
Benzema has been key to that run, the Frenchman scoring five goals now in three matches and even casting doubt on Gareth Bale’s place in the side.
“I am sorry for those who only discovered Benzema last week,” Solari said afterwards.
Bale has only just returned from a calf injury but was left out of the starting line-up, instead having to wait until the 67th minute to replace the in-form Vinicius Junior.
If Alex Granell’s free-kick had dropped into the far corner in the second minute, perhaps the contest would have been different but it clipped the crossbar and stayed out, much to the relief of Keylor Navas.
Marcelo should have doubled the lead after a brilliant Brazilian combination with Vinicius, who dragged the ball one way then the other into the full-back’s path. Marcelo nutmegged Marc Muniesa but failed to finish.
Vinicius was involved in Benzema’s second too, weaving in from the left and rolling inside. Benzema took one touch and curled it low, inside the far post.
Lucas Vazquez should have made it three after halftime but somehow managed to slice onto the post with the goal gaping.
Bale came on and tested Iraizoz from range but Girona pulled one back when Porro nipped in behind and slid a finish under Navas with 19 minutes left.
Porro rushed to collect the ball out of the net but the revival was short-lived. Llorente drilled a shot into the corner from 25 yards to keep Madrid’s resurgence rolling on.