Central defender Rami missed his side's surprise 2-1 defeat to AZ in the first leg in the Netherlands due to suspension, but returned in some style as Unai Emery's side coasted through with a 5-2 aggregate win.
AZ simply could not cope with the home team's movement and were undone by their inability to deal with numerous cross balls.
They fell behind on 15 minutes when Rami powered home a header from the impressive Sofiane Feghouli's delivery after AZ goalkeeper Esteban Alvarado came off his line, but failed to collect the cross by some margin.
Rami added a second goal two minutes later when he popped up unmarked to net after Roberto Soldado had flicked on a header from Tino Costa's cross.
Jordi Alba slipped the ball over the line from Soldado's cross on 56 minutes before substitute Pablo Hernandez sent a delightful shot swerving beyond Esteban to complete a 4-0 win that did not flatter the home team.
Valencia will face Atletico Madrid in all-Spanish semi-final after Atletico completed a 2-1 win at Hannover for a 4-2 aggregate success. The first leg is at Atletico's Estadio Vicente Calderón on April 19 with the return match at the Mestalla a week later.
With Athletic Bilbao progressing after a 6-4 aggregate win over Schalke, there remains the possibility of an all-Spanish final with Sporting Lisbon standing between Athletic and a place in the final.
AZ were lucky to get out of town shipping only four goals with Tino Costa knocking a volley wide from 12 yards on six minutes and Esteban saving from Soldado before Rami struck his first of the night.
The unmarked Rami drove home his second minutes later. He has now netted three of Valencia's previous five goals in the Europa League.
Diego Alves made a couple of decent saves from Adam Maher in the first period and Maarten Martens in the second half, but the action tended to be centred around the visiting goal.
Jonas headed narrowly wide from Jordi Alba's cross on 40 minutes before Alba scampered through the middle of the visiting defence only for Esteban to make a brave stop.
Jonas saw a shot hacked off the line seconds before Alba struck Valencia's third goal as the home fans were allowed to enjoy the closing moments of the match free from the possibility of extra-time.