Borja scored with his left foot into the high centre of the goal after intercepting a pass from Los Leones's Ibai Gómez.
With 42 points Azulones trail Real Betis by one for the final Europa League spot, and have compiled a record of 12 wins, 10 losses and six draws on the season. Los Leones are in 14th place, just five points above the relegation zone with a record of nine wins, 14 losses and five draws after 28 games.
Getafe had 38.2% of possession.
The seven attempts by Pedro León were the most of any Getafe player.
Alberto Lopo was brought on to replace Miguel Torres in the 26th minute when the latter went down with an injury.
Athletic Bilbao maintained control of the ball for 61.8% of the contest, a testament to their movement and linking play in the open field.
Los Rojiblancos won 55 duels and 14 headers, which led to eight shots, one of which were accurate.
Aritz Aduriz had four shots for Athletic Bilbao, more than any of his team-mates.
Gorka Iraizoz made seven saves for Los Leones.
Andoni Iraola's 16 passes to Borja Ekiza were the most between any Athletic Bilbao team-mates during the match.
- Sports & Recreation
- Athletic Bilbao