Falcao scored twice in the 3-0 victory in Romania in May and could have scored more at the Vicente Calderon as Bilbao continued to struggle without Spain internationals Fernando Llorente and Javi Martinez, who were omitted from the squad again with their futures at the Basque club uncertain.
Falcao opened after receiving a throw-in from Filipe Luis that he carried past defender Mikel San Jose before chipping goalkeeper Gorka Iraizoz for the 20th-minute opener in the Spanish league match.
The Colombia striker’s athleticism allowed him to meet Diego Godin’s looping cross at the far post with an acrobatic volley to make it 2-0 in the 42nd.
Falcao created the third as Carlos Gurpegui blocked his pass with his hand inside the area to set up a 59th-minute penalty the Atletico striker converted for his third goal.
Only Iraizoz kept Falcao and the rest of his Atletico teammates from adding to the scoreline with a number of clutch stops before Tiago completed the emphatic victory with a rising shot into the roof of the net in the 84th.
Athletic coach Marcelo Bielsa may find himself under pressure after conceding nine goals in two consecutive league losses, especially with Llorente and Martinez’s situation obviously distracting.
Meanwhile, promoted Valladolid joined Barcelona and Rayo Vallecano as the only teams with two straight wins to start the season after it scored both penalties in a 2-0 win over 10-man Levante.
Defender David Navarro handled inside the area for a second booking and red card to set up Victor Perez’s 38th-minute penalty at the Jose Zorrilla Stadium. Perez stepped up to score another spot kick in the 48th to secure the victory.