The winger provided a sublime finish worthy of Dean Parrett's 70-yard break for the opening goal before hitting a left-foot screamer into the top corner that flew in off the inside of the post on the stroke of half-time.
In-between, Jon Obika glanced home Tom Carroll's cross as the lads took a 3-0 lead into the break.
The team didn't hit the same heights in the second half but had the final word when Souleymane Coulibaly hit an equally-impressive goal - a dipper into the top corner from 20 yards - to complete the scoring in the 81st minute.
The match ended with Lawrence Vigouroux tipping over Sam Hoskins' fierce drive, a fitting finale to an impressive evening for the young goalkeeper whose clean handling from crosses was another highlight.
This was the team's fourth straight win - scoring 18 goals in those four games - and made it seven unbeaten as they top Group Two of the Barclays U21 Premier League.
Most of the key incidents in the first half were condensed into a 12-minute spell between 12 and 24 minutes.
We started at an electric pace and might have scored inside 20 seconds when Jordan Turnbull failed to deal with Falque's cross, but Cristian Ceballos couldn't connect with the loose ball with the goal gaping.
Southampton played their part and Jake Sinclair struck a low 20-yarder at Vigouroux before both teams fired into the side-netting, Falque from Ceballos' cross and then Hoskins after Ryan Seager missed an attempted flick in front of goal.
Then, in the space of seconds, Ceballos was inches away from Ryan Fredericks' cross and at the other end, Vigouroux did well to save at the feet of Hoskins.
The opener was a cracker. It all stemmed from a Southampton free-kick from the right byline that Vigouroux did well to punch clear. Falque flicked the clearance to Parrett on the edge of the box and he raced away, sprinting fully 70 yards and somehow keeping his feet from two lunging tackles to eventually roll the ball into the path of Falque, who curled first-time into the top corner.
Within seconds, Fredericks broke into the box and shot straight at Chris Jones and with the visitors on the rack, the second goal soon arrived. Carroll crossed from the right and Obika darted in front of Bevis Mugabe to glance the ball into the far corner.
Southampton steadied the ship for the for the next 20 minutes before our third goal right on the stroke of half-time.
This time Carroll spread the play wide right to Obika and he managed to pull the ball back to Falque, who took aim and drilled the ball into the top left corner from 20 yards.
The second half was an even affair notable for Vigouroux's performance in goal and another fantastic strike.
He was first called into serious action by Hoskins, a low save down to his left, before the same player burst through on goal only to be denied again, this time Vigouroux blocked the one-on-one chance with his legs.
At the other end, Obika fired wide, Ceballos curled a free-kick on target that was an easy take for Jones and Carroll skied an effort from substitute Alex Pritchard's pass.
The final word went to another substitute, Coulibaly, who was simply not going to be denied and with nine minutes remaining, picked the ball up on the left corner of the box and ripped a dipping shot over Jones into the far corner - all followed by his trademark celebration somersault.
Spurs (4-2-3-1): Vigouroux; Fredericks, Hall, Luongo, Stewart; Carroll, Mason; Falque, Parrett (Coulibaly, 68), Ceballos (Pritchard, 77); Obika. Unused subs: McGee, Veljkovic.
Southampton: Jones; Butterfield, Mugabe, Turnbull, Targett (Young, 79); Curtis, Moore (Gade, 69); Sinclair, Reeves, Isgrove (Seager, 10); Hoskins. Unused subs: Britt, McQueen.
Goals: Spurs - Falque (21, 45+2), Obika (24), Coulibaly (81).