The striker has struggled to impress his Manchester United manager in recent weeks amid concerns over his fitness, but he showed no signs of rustiness with an impressive display in Riffa.
Having previously not found the back of the net since late January, Falcao was among the goals before the break with two composed finishes – albeit against slack defending – while he also created the opener for Carlos Bacca.
Substitute Adrian Ramos added a fourth for Colombia after 59 minutes, while Johan Mojica and Andres Renteria completed the rout in the closing minutes after Falcao had been replaced.
Falcao's night had been productive enough as Colombia began their Copa America preparations in perfect style.
Keen to impress ahead of the tournament in Chile, the visitors applied pressure to the Bahrain goal from kick-off and were denied an opener as early as the sixth minute as Juan Cuadrado saw an effort thud against the post.
It did not take long for the deadlock to be broken, though, as Falcao took centre stage in all three goals before the break.
The on-loan Monaco striker rose to head down a Juan Quintero chip for strike partner Bacca in the 15th minute, and the Sevilla man lashed home from seven yards.
Colombia were in complete control of proceedings and the inevitable second goal duly arrived two minutes after the half hour, Falcao given plenty of time to compose himself inside the penalty area before firing past Sayed Jaafar.
The 29-year-old doubled his tally four minutes later as he raced through the centre of Bahrain's defence, his low effort deflecting off a defender on its way in.
Falcao's hat-trick should have arrived after 49 minutes as Bahrain failed to clear a free-kick, but the striker's lunge at the back post was not enough to seal his treble.
Two half-time substitutes then combined to extend Colombia's lead, Fredy Guarin sliding a pass into Ramos, who converted his second goal in as many international appearances.
Falcao's impressive display was brought to an end after 72 minutes, but Colombia were far from finished as Mojica and Renteria put a gloss on the win, capitalising on more poor defending with late goals.
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