The visitors got a penalty after an hour when Esteban Granero fouled Sergio Roberto in the penalty box. And it was youngster Oscar Menses who was the hero of the day as he netted the victor for the hosts in the 88th minute of the game.
Second-leg prospects: "The team that are ahead [going into the second leg] are the favourites".
"I congratulate them and we'll meet again in a week's time".
Speaking to fcbarcelona.com, Valverde said the saved penalty "may have been the turning point". "The second half was more competitive and Espanyol were better on the counter".More news: Palestinian Young Man Killed By Israeli In Jenin
"It was an open match, but they capitalized on their chances", Atletico coach Diego Simeone said. The defeat ended their unbeaten run of 29 games in all competitions.
Police said an Atletico fan in his early 20s was hospitalized in a serious but stable condition before the match after being stabbed in a fight near a metro station in the stadium area.
Goncalo Guedes and Rodrigo scored in the second half as Valencia came from behind to record a 2-1 win over La Liga strugglers Alaves. The visiting side went ahead through Ruben Sobrino in the 66th minute but Portugal worldwide Goncalo Guedes levelled for Valencia in the 73rd.
Forward Rodrigo scored the victor from close range, firing a shot that hit the post before going in.