With Barca flying at the top of La Liga and Espanyol mired in 14th, there was an obvious favorite here.
Shortly after the hour mark, Barca were awarded a penalty when Sergi Roberto was brought down.
Messi failed from the spot in the 62nd minute, his shot brilliantly saved by goalkeeper Diego Lopez. "In a week we'll see them at the Camp Nou". Espanyol could yet ruin their fiercest rivals dreams of a treble.
It was a rare miss for Messi, who is having a stellar season and is the Spanish league's top scorer with 17 goals.
However, despite the lack of clear-cut chances and the one-goal defeat, Ernesto Valverde wasn't too downbeat with the performance.More news: McDonald's Renews Sustainable Packaging Goals
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The Catalan giants were dealt a blow 10 minutes into the second half when Paulinho was forced off due to an injury. "We are lucky to have that game at home, and we will have to win whatever happens".
Leganes will host Real Madrid on Thursday in the first leg of the quarterfinal of the Copa del Rey.
Costa put Atletico ahead in the 73rd minute only for goalkeeper Miguel Angel Moya to inexplicably push a speculative cross that deflected off defender Lucas Hernandez into his own net. "They deserved the victory". In the last five games, Espanyol has won three games, drawn one game and lost one game whereas Barcelona has won four games and drawn one game.
Police said the 22-year-old man was attacked near a subway station where fans arrive for matches at the Wanda Metropolitano Stadium.
Forward Rodrigo scored the victor from close range, firing a shot that hit the post before going in.