Falcao struck in the 90th minute to keep up his prolific run of scoring and ensure that Atletico Madrid beat Real Sociedad 1-0 to match Barcelona at the top of La Liga.
The Colombian had little impact in the game as Sociedad worked hard to keep him quiet, but he struck a wonderful curling free-kick with virtually the last kick of the game. The match at the Anoeta looked set to finish in a draw until Falcao stepped up to strike home a 25-yard free-kick that left Sociedad goalkeeper Enaut Zubikarai grasping at thin air.
That was Falcao's 12th goal of the season in all competitions for Atletico and helped the Rojiblancos earn a sixth successive league victory that moved them back level on 22 points with Primera Division leaders Barcelona.
For Sociedad, the defeat ended their 100% home record this season and left them three points above the relegation zone.
Christhian Stuani's first goal for Espanyol deep into stoppage time handed the Catalans their first win of the season as they came from behind to beat Rayo Vallecano 3-2.
Leo Baptistao had headed Rayo into an early lead but two goals from Joan Verdu either side of half-time put Espanyol 2-1 in front before Leo slotted home his second of the game just after the hour mark.
However, after both sides had been reduced to 10-men as Diego Colotto and Mikel Labaka both saw red it was substitute Stuani who was the hero as he powered home Sergio Garcia's cross to bring relief to the Cornella El Prat.
Michel's stunning 35-yard strike three minutes from time handed Levante all three points from an otherwise turgid game as they beat Getafe 1-0 at the Alfonso Perez Coliseum.
Both goalkeepers had comfortably dealt with long-range efforts all afternoon as neither side looked capable of breaking the opposition down until the Levante substitute latched onto a loose ball just inside the Getafe half and took a touch before looping his effort over the helpless Miguel Angel Moya.
Juan Ignacio Martinez's men have now taken 13 points from their opening eight games, whilst Getafe slip back into the bottom half.
Real Zaragoza survived a late scare to beat 10-man Granada 2-1 at Nuevos Los Carmenes.
Helder Postiga headed the visitors in front from Victor Rodriguez's free-kick after just three minutes and the latter then added a second 25 minutes later with a simple finish from Abraham's cross.
Granada seemed dead and buried when Iriney was shown a straight red card for bringing down Apono midway through the second period, but they did manage to get a goal back with just over 10 minutes remaining when Youssef El-Arabi headed home from Fabian Orellana's corner.
And they should have equalised with virtually the last attack of the game when Inigo Lopez somehow failed to connect with Mikel Rico's cross.
Osasuna could not mark midfielder Patxi Punal's record-breaking appearance with victory as they were held in a 0-0 stalemate with Real Betis.
The 37-year-old Punal lined up in midfield to break the club's record of 463 appearances, but the match itself proved a largely frustrating experience as Betis stood firm, and the visitors would have won the match but for an assistant's flag denying Ruben Castro a first-half goal. The result leaves Osasuna still rooted to the foot of the table, while Betis missed the chance to push into the top four.
Information from the Press Association was used in this report