The Frenchman scored with a left-footed volley in the 73rd minute after Saul Niguez’s shot was deflected into his path, extending Atletico's unbeaten record to 12 games.
Atletico's Yannick Carrasco had forced a smart save from goalkeeper Diego Lopez as the visitors made the early running, though it was the Catalans who enjoyed the lion’s shareof possession during the first half without ever threatening.
After the break Pablo Piatti had a shot cleared off the line by Atletico defender Stefan Savic before the visitors went close through substitute Kevin Gameiro.
After Griezmann had put his side ahead, former Atletico striker Leo Baptistao was denied one-on-one by keeper Jan Oblak as Espanyol sought an immediate riposte, while Gerard Moreno put a header wide late on.
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Diego Simeone’s side sit three points ahead of fourth-placed Sevilla on 68 points, while Espanyol remain ninth with 49.
The Argentine coach was full of praise for his players after a week in which they also sealed a place in the Champions League semi-finals for the third time in four seasons.
“After midweek it was important to get the result here at a stadium where we always struggle,” Simeone said. “Espanyol are a tough opponent, they work hard as a team and can hit you on the break. In the first half we were not well organised but had more balance in the second.
“We have to keep doing what we do: defending well, working hard as a team and creating chances that allow us to win games. That’s our strength. It’s admirable what these players are doing. Granted, we can play a bit better -- but the side won.”
Sporting Gijon lost ground in their bid to escape the relegation zone, requiring two late goals to salvage a 2-2 draw against bottom-of-the-table Osasuna.
Sporting are four points behind fourth-from-bottom Leganes, who lost 2-1 to Villarreal, with five games to play while Osasuna are nine points from safety.
(Reporting by Joseph Cassinelli; Editing by Clare Fallon)
