The Colombian great struck in the 3-1 defeat of Cadiz on Sunday. Falcao also scored on debut against Getafe (3-0 win) and then in his second game against Athletic Club (1-2 win).
He is now Rayo Vallecano's second-ever player to score in his first three games in LaLiga.
The only other player to do this was Diego Costa in the 2011/12 season.
Victory over Cadiz sees Rayo Vallecano reach 13 points as they climb to fifth place.
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