Falcao scored twice in the opening half hour as Colombia booked their place in the quarter-finals of the Copa America with the simplest of wins over Bolivia in Santa Fe.
It was the first time in his international career the Porto striker had scored more than once in a match, and the rest of the game, which was over as a contest, was as much about his quest to complete his hat-trick as anything else.
He failed, but Colombia, who kept their seventh clean sheet in their last 10 matches, secured top spot in Group A, sending Bolivia out and leaving hosts Argentina needing a win over Costa Rica to secure second place.
Falcao opened the scoring in the 15th minute as he latched onto a straight pass from Dayro Moreno, his diagonal run taking him into the box where he slotted the ball past Carlos Erwin Arias.
Bolivia paid for their lack of adventure just before the half hour as they handed their opponents a second.
A midfield mix-up allowed Pablo Armero to surge into the left side of the penalty area, where he was scythed down by Santos Amador.
It was a clear-cut penalty and Falcao made the most of it, his stuttering run-up causing Arias to go early as he sent the ball down the middle.
Gustavo Ramos should have added a third before the break but he contrived to miss from close range after good work from Camilo Zuniga and Fredy Guarin.
The second half continued in a similar vain with Colombia dominating, playing neat football without creating many good chances.
Falcao went for his hat-trick after 64 minutes when substitute Hugo Rodallega laid the ball off, but the ball flashed wide - then a minute later Moreno chose to shoot, missing the target, when Falcao was lurking.
After 72 minutes Colombia came mightily close to adding a third when an intricate move involving Gustavo and Armero ended with Rodallega shooting for goal. Falcao, desperate for his hat-trick, stuck out a foot and deflected the ball wide.
Falcao had another chance for a third six minutes from time when Juan Cuadrado's cross found him at the far post, but he could not jump high enough and headed over.