La Roja entered the match three points clear of second-placed Italy, and with the Azzurri being held to a 1-1 draw by Macedonia, Julen Lopetegui's side have secured their position in the finals with one match to spare.
Spain will travel to Israel on Monday for their final Group G clash as Italy, who are almost certain of a spot in the playoffs, finish away to Albania on the same night.
The big team news in the Spain camp was that there was an international debut for Real Sociedad defender Alvaro Odriozola, while Valencia's Rodrigo was handed a forward position alongside Isco and David Silva.
Spain's first half-chance of the night arrived in the seventh minute when Jordi Alba broke down the left before delivering a dangerous cross into Rodrigo, but the 26-year-old could not produce a shot on target.
It was Albania that registered the game's first shot on target in the ninth minute when Eros Grezda broke into a dangerous position, but the number 17's effort was never troubling Manchester United goalkeeper David de Gea.
Rodrigo had a golden opportunity to send Spain ahead in the 13th minute after meeting a brilliant cross from Isco, but the forward somehow headed wide of the post from close range as Albania struggled to contain the hosts.
Rodrigo made no mistake three minutes later, however, as the Brazilian-born attacker controlled an Isco pass with his chest before finding the far corner with a wonderful finish.
Spain then doubled their lead in the 24th minute when Isco collected a cute pass from Koke before drilling the ball into the roof of the net as Albania struggled to cope with a brilliant start from Lopetegui's side.
Albania actually hit the crossbar through a Llullaku header in the 25th minute, but the visitors were 3-0 behind moments later when Thiago Alcantara rose highest inside the penalty area to head a floated Odriozola cross into the back of the net.
Silva headed an Isco flick over the crossbar just past the 30-minute mark as Spain continued to threaten, before Alba sent a low effort just wide during a period of utter domination from Lopetegui's team.
Rodrigo then headed another Odriozola cross over the Albania crossbar five minutes before the break as Spain threatened to run riot.
Albania actually had a golden chance to get their name on the scoresheet in first-half stoppage time when Grezda robbed Gerard Pique inside the Spain box before attempting to find Llullaku, but Ramos was across to make a fine clearance.
Rodrigo was next to come close for La Roja after meeting a through-pass from Silva, but the forward could not beat Berisha, who had a busy start to the second period.
Arlind Ajeti had Albania's first chance of the second half after meeting a corner from the right, but the centre-back's header missed the post.
Armando Sadiku then had an even better opportunity in the 69th minute after rising highest inside the Spain box, but the substitute's header hit the post as the home side survived another dangerous moment.
Albania had two more opportunities three minutes later, and De Gea had to be alert to keep out a strike from Liridon Latifi, before Sadiku fired the rebound over the crossbar.
Marco Asensio followed Nacho off the Spain bench as the match headed for its final 15 minutes, and the hosts appeared to go up a gear as Saul sent one just wide of the Albanian post in the 78th minute.
Asensio also came close with a free kick in the latter stages, but 3-0 was how it ended as Spain confirmed their spot at the 2018 World Cup courtesy of Macedonia's late goal in Italy.