The Blaugrana were denied a dream start by the crossbar as Gerard Pique’s header from a corner crashed off the woodwork.
However, Ter Stegen was quickly called into action as Mario Gaspar whipped a cross into Barca’s box for Roberto Soriano, whose first-time volley was parried away by the German.
Soriano was particularly dangerous in behind Cedric Bakambu, and the Italian curled a shot just wide, before Lionel Messi – with only one goal in seven games – couldn’t guide his daisy-cutter on target.
Jaume Costa then angled a cross into the visitors’ six-yard box, but Ter Stegen punched it away before Soriano could throw himself at the ball.
The game appeared destined for stalemate after Messi knocked Alba’s one-two wide of the far post, yet Dani Raba flew recklessly into Sergio Busquets with his studs up to leave Villarreal a man down.
That, combined with Aleix Vidal’s introduction, clicked Barca into gear, and Suarez suddenly grazed the woodwork from Alba’s cross into the six-yard box.
Nonetheless, he proceeded to play a give-and-go with Paco Alcacer, before quickly rounding Sergio Asenjo for his 50th away goal in a Blaugrana shirt.
Manuel Trigueros almost pulled one back for the home side when he let fly from 25 yards out, but his effort stung the palms of Ter Stegen.
Any hopes of a comeback were extinguished by an awful backpass, which gifted Messi the chance to blast the ball home for his 14th League goal of the season.
The Argentine was probably too selfless when he laid off the substitute to his right in Villarreal’s box, but his low strike was blocked by Asenjo.
