Malick Yalcouyeās fourth goal of the season secured a deserved second league stage win for Albion in the UEFA Conference League.
Yalcouye scored with a close-range header midway through a second half which Albion dominated.
Fabian Hurzelerās side have yet to concede a goal in five games in the competition and they have now lost just once in their last 13 games.
Malick Yalcouye heads in the only goal.
This was an utterly professional performance by Albion. They drew the sting out of Getafe in the early stages and after the break had the chances to add to their goal.
The hosts, currently 13th in La Liga, made a predictably fast start without troubling Bart Verbruggen and Albion gradually settled into their work.
Georginio was off target with two efforts but did well down the left before pulling the ball across the face of goal. At full stretch Yasin Ayari failed to make contact at the far post.Ā
Lewis Dunk gets up to head clear his lines. š·James Boardman
There wasnāt much pattern to either sideās play in the opening half hour but Verbruggen was called upon to get down and keep out Ivan Azonās close-range shot with a strong left hand. It was his only save of the night.
Albion should have scored in the 38th minute.
Jaouen Hadjam was in the inside right channel when Rutter picked out his run and as Azon came out of goal then hesitated he flicked the ball beyond the keeper and against the post. Hadjam pulled the rebound back to Yalcouye, but his shot was blocked on the line by Johan Mojica.
Yasin Ayari just can't reach Georginio's inviting cross. š·James Boardman
Hadjam had an impressive night, getting forward again early in the second half and bending a shot from the edge of the box that kissed the crossbar with Azon beaten.
Half-time substitute Luka Vuskovic wasnāt far away with a right-foot drive from 25 yards that curled just wide of the right-hand post. It felt like an Albion goal was coming and it arrived in the 64th minute.Ā
Costinha created it with a header into the box from the right and Yalcouye met it perfectly with a header from close range that bounced up and in off the underside of the crossbar.Ā
The Albion line-up before kick-off at the Estadio Coliseum. š·James Boardman
In their next attack Georginio showed strength and skill to shake off Djene Dakonam and burst into the box, but with an unmarked Pascal Gross waiting for a tap-in he elected to shoot and failed to test Azon.
Two subs combined with 12 minutes to go but Ibrahim Osman couldnāt find the target when he slid in to try and convert Diego Gomezās cross from the right.
However, Albion had done enough and the travelling fans were loud and proud at the end as they acknowledged Hurzeler and his players for a professional job done.
Albion: Verbruggen, Costinha, Dunk (Vuskovic 45), Svoboda, Boscagli (Osman 78), Hadjam (De Cuyper 70), Gross (Gomez 70),, Ayari, Hinshelwood, Rutter, Yalcouye.Ā
Subs not used: Steele, McGill, Nti, Kostoulas, Ibrahim.