Following a slow start to the match, Tottenham's cause was not helped when striker Jermain Defoe came off after just eight minutes with what appeared to be a hamstring strain.
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Moments later it was almost two when Falcao finished off at the second attempt without realising that the linesman's flag had been raised for offside.
The hosts went in leading by one goal at the break and made a pair of changes at half time. One of the substitutes, Lucas Ocampos, made an instant impact by doubling Monaco's advantage minutes after the interval with a glancing header.
It was soon 3-0 when Falcao collected Ocampos's pass and made no mistake in front of goal.
Spurs pulled one back in the 57th minute when Defoe's replacement, Harry Kane, took advantage of a loose ball in the area by sliding home.
Monaco's three-goal lead was restored soon after when Falcao got his second, again receiving a pass from Ocampos before finding the back of the net.
The Ligue 1 outfit had five in the 70th minute. The home side broke with pace and Mounir Obbadi rounded off the counter-attack by drilling low past Lloris.
Monaco could have made it six before the end but it was the visitors who scored the seventh goal of the match when Andros Townsend skipped past a couple of challenges and fizzed low into the corner from 25 yards.