With full backs Jordi Alba and Sergi Roberto injured, Spain coach Julen Lopetegui included Arsenal's Nacho Monreal to form an unusual back three with Sergio Ramos and Gerard Pique.
A midfield four gave Spain superiority in that area of the pitch and they monopolised possession but were met with dogged opposition by Gianni de Biasi's side, who went into the game top of the group after winning their opening two games.
The visitors' best first-half chance was a drilled effort by Vitolo from the edge of the area tipped away by Etrit Berisha, though the Atalanta keeper ended up gifting Spain their opener.
His misplaced pass landed at the feet of Vitolo, who quickly found David Silva to tee up Costa for a close range tap in.
With the wind finally in their sails after a frustrating first half, Spain turned on the style and doubled the lead when Nolito curled Monreal's cut back into the far corner.
STRONG POSITION
Spain lead the group with seven points due to a better goal difference than Italy, who snatched a late 3-2 win at Macedonia. Albania stayed on six points and slipped from first to third.
The Spaniards are now in a strong position in the section after taking four points from their two trickiest away games, their latest win coming three days after a 1-1 draw in Italy.
"We knew this game would be very difficult and good teams like France have lost here recently, but we managed to minimise Albania," Lopetegui told a news conference.
"These were two difficult away trips and we're satisfied with the results, but we know we're in for a long qualifying campaign."
Spain captain and Real Madrid defender Ramos limped off with 10 minutes remaining suffering from a suspected knee injury, the one negative of a satisfying night for Lopetegui's side.
"We think it's a strain and we hope it's nothing important," added the coach. Spanish media said Ramos could be out of action for a month.
(Reporting by Richard Martin; Editing by Ken Ferris)
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