A 12th minute header from Raul Garcia proved to be enough for the hosts, much to the delight of coach Diego Simeone and the home faithful at the Vincente Calderon.The win stretches Atleti's unbeaten run at home to 18 league games and opened up a four point lead at the top of the table.
That gap was cut to one by second-placed Barcelona later on Saturday, as the Catalan club secured a 3-1 win over Real Betis at the Camp Nou to end a difficult week on a high note.
The reigning champions hit the headlines for the wrong reasons after being hit with a transfer embargo by FIFA for next season in relation to irregularities in their youth setup.
Any suggestions of Gerado Martino's side being distracted by those events were banished after 15 minutes, when Lionel Messi stroked home a well-struck penalty, following a foul from Jordi Figueras on Alexis Sanchez.
It went from bad to worse for Figueras, who put the ball into his own net after attempting to cut out an Adriano cross after 67 minutes.
Betis were handed a lifeline just a minute later, when Ruben Castro turned in Alfred N'Diaye's cutback, setting up a nervy finish for Martino's men, but any hopes of a comeback were extinguished four minutes from time, when Juanfran was adjudged to have handled Neymar's cross in the box.
Messi saw his resulting spot-kick saved by Adnan but was first to the rebound to wrap up a hard-fought win.
That left third-placed Real Madrid in need of a win to stay in touch with the top two at Real Sociedad.
Former Sociedad midfielder Asier Illarramendi gave Madrid the lead just before half time, poking home Karim Benzema's effort that was well saved by Claudio Bravo.
That lead was doubled after 66 minutes when Gareth Bale took advantage of Bravo's poor kick to smash home from 30 yards, before Pepe added a third late on.
Angel Di Maria came off the bench to extend his side's lead further two minutes from time, following some terrific link-up play with Alvaro Morata, completing a convincing win for the visitors.
In the day's only other game, 10-man Rayo Vallecano gave their survival hopes another significant boost with a 3-0 win at home to Celta Vigo, courtesy of a second-half brace from Alberto Bueno, who added to Ruben Rochina's 26th minute opener.
Razvan Rat saw red for an off the ball incident after 64 minutes but it failed to have an impact on proceedings as Paco Jemez's side held on for their fifth straight home win.
