Earlier Thursday, Espanyol overturned a 2-1 loss in the first leg to defeat Levante 2-0 with Leo Baptistao and Gerard Moreno on target either side of half-time.
Ernesto Valverde's side are next in action on Thursday at home to Celta in the second leg of their last-16 Copa del Rey tie - the first leg having ended 1-1 - but Umtiti is not expected to be available.
"I would say I'd prefer not to draw Real Madrid", Valverde admitted in his news conference after the game.
Suarez pounced on a mistake to make it 4-0 before the interval and leave club-record signing Philippe Coutinho applauding from his seat in the stands.
The Argentine then set up Alba with a sublime pass to slide home their third goal, before Luis Suarez scored from Celta defender's poor back-pass before the break.
"It's a luxury to have him in the team", Alba told Gol Television.
It was 2-0 two minutes later when Alba and Messi combined once again with the latter scoring with a first-time finish.
"We always look for each other to score goals and today we have done it twice".
A 1-1 draw from the first match in Galicia had left the tie looking open, but a devastating first-half performance from the holders secured their 6-1 aggregate victory.