Atletico suffered a lot in the first half but pulled level with a deflected header from Marcos Llorente which enraged the visitors as the goal came in the second minute of added time when only one minute was supposed to be played.
The hosts kicked on after the interval and top scorer Luis Suarez drew a foul from Unai Nunez to win a penalty and dusted himself down to confidently dispatch his spot-kick and claim an 18th league goal this season.
Suarez was then left frustrated as he was taken off in a series of defensive substitutions from coach Diego Simeone, who also removed record signing Joao Felix and winger Thomas Lemar in favour of midfielders Lucas Torreira and Saul Niguez before introducing Geoffrey Kondogbia to further grind out the win.
Athletic defender Nunez could have snatched an equaliser in added time but headed straight into the arms of Oblak and Atletico saw out the victory to move on to 62 points from 26 games.
"We really struggled in the first half, they were all over us and we kept getting pushed back but our first goal gave us strength," Llorente said.
Atletico had conceded a late equaliser to draw 1-1 in Sunday's derby with Real Madrid, but knew they had another chance to gain ground on both main rivals in this game in hand.
"We see every game as special but we were really looking forward to this one, it was very important for our confidence," said Llorente, who also defended his side's conservative tactics.
"The key thing is to adapt to every type of pressure. There are moments when you cannot be pressing high up the pitch."