Atleti had Ghana midfielder Thomas Partey in their starting line up after he missed the 3-0 Champions League round of 16 clash against Juventus on Tuesday.
Inaki Williams put the home side in front in the 73rd minute, guiding the ball into an empty net. His 14th goal of the season.
Kenan Kodro sealed the win for Athletic five minutes from time with a shot which took a huge deflection off Gimenez.
Atletico are second in the standings on 56 points while Barca have 63 and can increase their advantage at the top when they visit Real Betis on Sunday.
Bilbao are ninth on the tabl