The visitors finally got Antoine Griezmann into the game in the 64th minute after being sent through the middle but his first-time strike was off the mark.
The rumours have refused to go away, however, and a man who recently passed 100 goals for Atletico is now being heavily linked with a summer switch to Camp Nou. He's scored more against them than any other side, excluding Sevilla, and his first-half free kick was his 28th goal against them 36 games.
A month ago, Barcelona was 11 points clear at the top and appeared to have a clear path to the title.
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"We're going to have to look after him very closely".
But now the snarling, aggressive and brutally effective presence of Costa - every central defender's worst nightmare - is finally giving Griezmann some support, providing a focal point of the attack which the Frenchman can play around and feed off, rather than having to do it all by himself.
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Atletico coach Diego Simeone said the league was Barcelona's to win.
The build-up to this contest, labelled "the Grand Final" by sections of the Spanish press, was driven by talk of a Barcelona dip following three draws in five league games, with the in-form Atletico primed to move within two points of their rivals. Costa, however, had strayed offside and Barca held on for what will surely prove a crucial three points.
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Barca had the "MSN" (Messi, Suarez, Neymar) and Real Madrid still have the "BBC" (Gareth Bale, Karim Benzema and Cristiano Ronaldo), but there's been a new acronym-powered frontline in La Liga since January: "AG-DC". "But we have made it possible". But despite finally getting close to Barca's goal, Marc-Andre ter Stegen was rarely called into action.