Falcao scored his fourth goal of the season in the 56th minute to give Atletico Madrid a four-goal lead, and it turned out to be the match-winner in a 4-3 win over Rayo Vallecano on Sunday in La Liga.
Mario Suarez scored in the opening half for Atletico and goals from Koke, Arda Turan and Falcao in a seven-minute stretch early in the second half put Madrid in complete control at the Vicente Calderon.
But Andrija Delibasic scored a brace in a three-minute stretch and Leo notched a third goal in just a seven-minute span as Rayo Vallecano notched three goals in the final 10 minutes to leave the result in doubt.
Atletico managed to hold on for its second straight win, as it stayed unbeaten through three matches this season.
Vallecano opened the season with consecutive wins and tied its third game, but suffered its first loss of the season as its amazing comeback fell just short.
Espanyol 3, Athletic Bilbao 3
Barcelona, Spain - Aritz Aduriz scored his second goal seven minutes from time as Athletic Bilbao tied Espanyol, 3-3, on Sunday at Estadi Cornella-El Prat in La Liga.
Bilbao notched all three goals in the second half to rally twice, first from a two-goal deficit on strikes from Aduriz and Fernando Llorente and again in the 83rd minute when Aduriz completed his brace.
Javi Lopez and Verdu scored in the first half to give Espanyol a two-goal lead and Samuele Longo restored a one-goal cushion in the 80th, but was sent off in the 81st.
Bilbao responded for the final time just two minutes after getting the one-man advantage, and secured a point on the road.
Espanyol lost its first three matches, but earned its first point.
Granada 1, Deportivo 1
Granada, Spain - Antonio Floro Flores scored nine minutes from time as Granada earned a 1-1 draw against Deportivo on Sunday at Los Carmenes in La Liga.
Nelson Oliveira scored late in the first half for Deportivo, which is unbeaten with a win and three draws this season.
Granada earned its second point with its second draw in its last three games.
Osasuna 1, Mallorca 1
Navarra, Spain - Tomer Hemed scored his fourth goal of the season with just 12 minutes remaining as Mallorca tied Osasuna, 1-1, on Sunday in La Liga at the Estadio El Sadar.
Osasuna and Mallorca both had a player sent off in the first half, and Osasuna took the lead through Kike Sola in the 69th. Hemed followed in the 78th as his side earned a point.
After starting the season with three straight losses, Osasuna earned its first point.
Real Sociedad 2, Real Zaragoza 0
San Sebastian, Spain - Inigo Martinez and Carlos Vela scored six minutes apart early in the second half as Real Sociedad downed Real Zaragoza, 2-0, on Sunday at the Anoeta in La Liga.
Sociedad won for the second time in its last three games, while Zaragoza lost for the third time through four matches.