In an otherwise unremarkable game, Griezmann proved decisive from the penalty spot in the 56th minute after Koke had been felled by a wild Esteban Granero kick.
It was Griezmann's 86th La Liga goal for Atletico in his 160th outing since joining from Real Sociedad in 2013.
He also scored 40 La Liga goals for La Real across four seasons in the top flight, plus six in the second tier in 2009-10.
In total, 26 of Griezmann's goals have come for his country, four of which were scored in this year's World Cup.
Atletico are well in the title race, too, with their victory over Espanyol taking them level on points with leaders Barcelona at the top of La Liga, prior to the Catalan giants' clash with Celta Vigo.
"I can still improve, I am not at my best level, it has been a long year and sometimes I lack speed," he told reporters.
"I'm very happy to be able to help the team. It's a very long year, we have a game and then a little rest, there are games when it is difficult to be loose and fast, today was a day like that but I was able to score two goals."