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Atletico had leading scorer Radamel Falcao back from injury but it was combative striker Costa who scored from close range in a bruising encounter against Betis.
Another ruthlessly efficient performance ensured Diego Simeone's side made it 12 wins from 12 in the league at the Calderon with only six goals conceded.
Earlier, fourth-placed Malaga failed to make the most of Real's slip-up when they could only manage a 1-1 draw at home to Real Zaragoza to move on to 36 points.
They had to come from behind after Helder Postiga's 13th-minute volley put the visitors ahead at a sun-drenched Rosaleda.
Young playmaker Isco, who agreed an improved contract with the south-coast club during the week, levelled from the penalty spot in the 23rd minute and both sides hit the woodwork.
Manuel Pellegrini's side never really had complete control of the game, and there was no fairytale return for Brazilian forward Julio Baptista, who came on as a second-half substitute after some 15 months on the sidelines with injury.
Zaragoza had midfielder Jose Mari sent off for a second bookable offence near the end.
Rayo Vallecano also failed to close on the top sides when they lost 2-1 at improving King's Cup semi-finalists Sevilla.
Ivan Rakitic, who was later sent off, lobbed their opener from 35 yards out and Alvaro Negredo backheeled a cheeky second after Rayo had levelled from the penalty spot.
Betis are fifth with 35 points, Valencia sixth on 34, the same as seventh-placed Rayo, and Real Sociedad are eighth with 33 after a 3-0 home win over 10-man Real Mallorca.
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