Griezmann won the ball back in the Cordoba half to open the scoring inside five minutes, and then Saul marked his return from injury with a headed goal shortly before half-time, with the Andalusians unable to prevent a 10th straight defeat.
Atletico move on to 62 points thanks to the win, four ahead of Sevila, who recorded a sixth straight win in all competitions as first-half goals from Aleix Vidal and Carlos Bacca saw them past Athletic Bilbao 2-0.
Vidal pounced on a defensive lapse by the visitors to put his side ahead inside three minutes before Bacca demonstrated his physical presence to double the hosts’ advantage midway through the first half.
A fourth La Liga win in a row ensured Unai Emery’s side kept the pressure on fellow Champions League chasers Atletico and Valencia, bringing an end to Athletic’s five-game winning streak.
Meanwhile, David Barral scored a hat-trick as Levante thrashed fellow strugglers Almeria 4-1 away from home to move five points above the relegation zone.
Barral opened the scoring after 17 minutes and then, after his strike partner Victor Casadesus doubled the lead, notched his second to make it 3-0 eight minutes after the break.
Almeria defender Sebastian Dubarbier was then sent off for picking up a second booking but Tomer Hemed gave the hosts brief hope when he scored from the penalty spot. However, Barral soon killed off any chance of a fightback by
completing his treble.
Malaga and Real Sociedad drew 1-1 in the late kick-off, Ruben Pardo striking seven minutes from time to earn the visitors a share of the spoils after Recio had put Malaga in front 10 minutes into the second half.