In a poor game marred by play-acting and littered with fouls and cards, Colombia striker Radamel Falcao had the best chance for the visitors just after the hour when his low shot was well saved by goalkeeper Jordi Codina.
Midfielder Mario Suarez picked up a second yellow card in the 72nd minute for handling the ball and centre-back Diego Godin was dismissed in stoppage time after receiving a second booking for a high elbow.
Atletico have 62 points with eight games left, with champions Real on 65 after their 5-1 win at home to Levante on Saturday.
Real Sociedad, 4-2 winners at home to Malaga on Saturday, are 11 points behind Atletico in fourth. The top three qualify for the Champions League and the next best team goes through to the preliminary round.
"The lads are making a huge effort. They have had an impressive season and we have to keep the effort up for the last eight games," Atletico coach Diego Simeone told a news conference.
Argentine Simeone has transformed the team since taking over midway through last season.
Valencia climbed above Malaga and Real Betis into fifth place, two points ahead of the two Andalusian clubs on 49, after a goal from Jonas in the third minute of added time secured a 2-1 win at home to 10-man Real Valladolid.
Valladolid defender Mikel Balenziaga put the ball into his own net at a 38th-minute corner before centre-back Henrique Sereno was shown a second yellow card for felling Roberto Soldado in the area 12 minutes after the break.
Soldado picked himself up to take the spot-kick but it was saved by Valladolid keeper Dani Hernandez.
Oscar Gonzalez equalised in the 71st minute with a superb first-time shot that rocketed into the top corner.
Time looked to have run out for the home side until substitute Jonathan Viera fired over a cross and Jonas nodded the ball into the far corner.
Europa League qualification hopefuls Getafe are eighth, level on 44 points with ninth-placed Rayo Vallecano who won 2-0 at Celta Vigo.
Resurgent Espanyol moved up to 11th after recording a 2-0 win at Osasuna.
Leaders Barcelona maintained their 13-point advantage over Real Madrid with a 5-0 drubbing of bottom club Real Mallorca on Saturday as they closed in on a fourth title in five years.
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