Despite suffering a 2-1 reversal in the opening fixture in Holland last week, the Spaniards were on top form with Jordi Alba and Pablo Hernandez adding to Rami's early brace to wrap up an emphatic win on the night, and a 5-2 aggregate success.
Valencia did not enter the game in the best of shape having failed to win in four games, but they immediately pressured the AZ back-line with a fourth-minute Alberto Costa shot which flashed just wide.
Roberto Soldado saw his 12th-minute effort parried by AZ goalkeeper Esteban Alvarado, but two minutes later Frenchman Rami grabbed his side's opener when he finished off a Sofiane Feghouli cross from the right.
Two minutes later Valencia had grabbed the aggregate lead with another clinical close-range finish from Rami after Soldado had headed down a cross from the left from Costa.
Soldado shot wide two minutes later but AZ reminded their hosts of their danger in the 24th minute when Adam Maher came agonisingly close with a 25-yard effort which was tipped over by Valencia goalkeeper Diego Alves.
Soldado and Mehmet Topal both fired wide as the home side resumed control, and the Dutchmen had to wait until five minutes before half-time for another chance, with Brett Holman firing over the bar from long-range.
Alvarado got down brilliantly to deny Soldado in the 42nd minute and Soldado came close yet again seven minutes into the second half when his header from six yards was blocked by Niklas Moisander.
The third goal duly arrived in the 56th minute when Alba swept home from six yards after being played in by Soldado, extending the aggregate lead of Unai Emery's side to 4-2.
Maarten Martens forced a save out of Alves in the 70th minute but AZ could muster little in response before Valencia grabbed their fourth in the 80th minute, Hernandez blasting high into the top corner from a cross by Alba.