The £52million Colombia striker scored his brace in the second half as Spurs shipped a further four goals, having only been 1-0 down at the break.
It was a chastening evening for Andre Villas-Boas, who was without the in-demand Gareth Bale and several other senior players through injury.
Tottenham lined up with a back four of Kyle Walker, Jake Livermore, Zeki Fryers and Danny Rose, and with Falcao and another big-money buy James Rodriguez starting in attack for the hosts, the youngsters were always going to be in for a difficult evening.
And the task looked even tougher for Spurs when Jermain Defoe was withdrawn after just 10 minutes with what looked like a hamstring injury. The England striker was replaced by Harry Kane.
Surprisingly, it was Hugo Lloris and not his inexperienced defence who made the first error leading to a goal. After a free-kick for a foul by Walker, the ball was moved from left to right by James and right-back Andrea Raggi hit a volley which bounced and then went in at the France goalkeeper's near post.
Monaco had a goal disallowed after an intelligent step up from Rose resulted in a raised flag for offside, and Spurs were able to go in at the break only one goal down.
However, within five minutes of the restart, the hosts had scored twice more. First, substitute Lucas Ocampos glanced home a header from Joao Moutinho's free-kick and then Falcao arrived in the centre to meet Ocampos' cross from the right flank.
A defensive mistake from Nicolas Isimat-Mirin allowed Kane to reduce the deficit on 57 minutes, but it did not take long for the Ocampos-Falcao connection to produce another goal - again from a right-wing delivery.
Monaco's impressive Belgium Under-21 winger Yannick Ferreira Carrasco outshone his countryman Nacer Chadli, who was making his first appearance in a Spurs shirt, and his through-ball was tucked home by Mounir Obbadi for Monaco's fifth goal on 71 minutes.
There was still time for substitute Andros Townsend to find the net with an impressive solo effort, coming in off the right wing and firing in low from 20 yards.
Spurs complete their pre-season preparations with a home friendly against Espanyol next Saturday evening before travelling across the capital to Crystal Palace for their Premier League season opener on Sunday, August 18.