Javier Irureta's charges moved to within eight points of leaders Real Sociedad with the gritty success at Riazor.
Bilbao forged ahead just after the interval through Santiago Ezquerro but Depor immediately hit back with Donato levelling the scores.
The match appeared to be petering out towards a stalemate but Hector popped up six minutes from time to pinch the points for the hosts.
Real Betis remain in the hunt for a Champions League berth after Joaquin's last gasp strike breached Racing's rearguard in Santander.
Walter Pandiani spared Mallorca's blushes with an 81st minute penalty at home to struggling Recreativo.
The bottom club took a surprise lead on 55 minutes through Raul Molina's effort but Pandiani's spot kick earned his side a point in a match which saw seven Recreativo players booked.
Valladolid jumped into the top half of the table with a 1-0 triumph at Rayo Vallecano, courtesy of Oscar Gonzales's early strike.
Alaves were denied a much-needed three points by John Aloisi's 88th minute equaliser for Osasuna.
Adrian Ilie gave Alaves the lead before half-time but former Coventry striker Aloisi nicked a priceless point for the visitors.
Espanyol remain entrenched in the relegation zone after a 0-0 draw at Villarreal.
Click below for an individual match summary:
Alaves 1-1 Osasuna
Deportivo 2-1 Ath Bilbao
Mallorca 1-1 Recreativo
Racing Santander 0-1 Betis
Rayo Vallecano 0-1 Valladolid
Villarreal 0-0 Espanyol
