The hosts could have gone in ahead at the break when they were awarded a penalty in the 35th minute. However, Iker Muniain failed to convert as the sides went in goalless.
Javier Martinez nearly gave Bilbao the lead with 20 minutes to play, but his header cannoned back off the bar.
The home team made the breakthrough just minutes later as Muniain made amends for his earlier miss when he played in Oscar De Marcos, who fired in.
As Bilbao looked to have secured the three points, Alberto Lora converted in the 90th minute to earn Gijon a point.
The draw has kept Marcelo Bielsa's side 10th in the Primera Division table, while Gijon have moved one place up into 18th.