The Argentina international this season looks a player reborn under Mauricio Pochettino and the winger completed his treble in just 37 minutes, before Tom Carroll added a late fourth following Stephan El Shaarawy's second-half consolation.
The victory means Spurs qualify top of Group J and will now be seeded in the last 32, where they can meet the other groups' runners-up or one of the four unseeded teams that dropped out of the Champions League.
The reward may seem slight given the likes of Valencia, Sevilla and Galatasaray could still lie in wait, but Pochettino will take great satisfaction from a night which saw the likes of Harry Kane rested and fringe players step up to the plate.
Joshua Onomah, an 18-year-old academy product from Enfield, impressed on his first start for the club, while the out-of-favour Carroll made a timely case for more regular inclusion.
The stand-out name, however, was Lamela, who was as creative as he was clinical and appears finally to be delivering on the talent that persuaded Daniel Levy to pay upwards of £26million for him two years ago.
His first goal came inside two minutes as Clinton Njie fed Ben Davies on the overlap and the full-back's low cross picked out the Argentine, who side-footed home his first of the night with ease.
It was the perfect start for Pochettino's men, who cruised through the opening 15 minutes and soon doubled their advantage as Lamela's long shot skidded off the wet turf and underneath the body of keeper Danijel Subasic.
Monaco still failed to respond and it was almost three moments later as Son Heung-min finished off a one-on-one, but the visitors were spared as the forward had strayed just offside.
The respite was temporary, however, as Onomah's bursting run through midfield finally saw Carroll teed up on the edge of the area, but the midfielder's bending effort flew narrowly over.
Monaco were happy to pour forward when the occasional attack presented itself but they left gaping holes behind them, which Lamela, Son and Njie exploited on the counter.
One such break saw Son slip Lamela through again and, despite Jeremy Toulalan scrambling across, the 23-year-old drove first time past Subasic to complete his quickfire treble.
Tottenham's ascendancy was so marked that when Eric Dier momentarily took treatment on a knock to his foot, Pochettino instantly replaced him with Nabil Bentaleb, who made his first Spurs appearance in just over three months.
"I'm fine," Dier told his manager as he came off but this was no longer a night for risk-taking.
Bentaleb looked rusty, giving away possession at the start of the second half, but Tottenham still looked most likely to score as Onomah's close range effort was saved by Subasic.
The contest began to drift and Monaco startled a dozing crowd just after the hour mark, when El Shaarawy's long range strike found its way into the bottom corner.
Unperturbed, Pochettino replaced Lamela and then Njie - noticeably leaving Andros Townsend on the bench as the winger's exit in January appears ever more inevitable.
There was still time for a final flourish as Carroll, another academy graduate, capitalised on more inept Monaco defending, dancing all the way to the line before slotting home his first senior goal for the club to cap a comfortable night at White Hart Lane.
TWEET OF THE MATCH
"Spurs have been very good, Lamela starting to show his Talent at Last ! Monaco struggling sold too many players in the Summer" - former Tottenham and Monaco player Glenn Hoddle
PLAYER RATINGS
Tottenham
Hugo Lloris: 6 (out of 10)
Kieran Trippier: 6
Toby Alderweireld: 7
Kevin Wimmer: 6
Ben Davies: 7
Eric Dier: 6
Tom Carroll: 8
Erik Lamela: 9
Joshua Onomah: 8
Clinton Njie: 7
Son Heung-min: 8
Subs
Nabil Bentaleb (for Dier, 42): 6
Nacer Chadli (for Lamela, 62): 7
Dele Alli (for Njie, 79): 6
STAR PLAYER
Erik Lamela: The Argentina international came close to leaving White Hart Lane in the summer but he finally appears to be fulfilling his potential, completing a first-half hat-trick in just 37 minutes.
MOMENT OF THE MATCH
Tom Carroll has been on loan at Leyton Orient, Derby, QPR and Swansea, but the Spurs academy graduate capped an excellent display with his first senior goal for the club
Weaving his way through the Monaco defence, the 23-year-old finished from an acute angle before being swamped by his team-mates.
VIEW FROM THE BENCH
Mauricio Pochettino will be pleased to have finished top of Group J, securing their place amongst the seeded sides a nd a return home leg in the last 32
It was also the first time this season that the Spurs boss has not needed to call upon Harry Kane and he will have been relieved to have given the striker a rest with the Christmas schedule fast approaching
MOAN OF THE MATCH
Whatever happened to Joao Moutinho? One of the last remaining stars of Monaco's financial splurge and once renowned throughout Europe for his playmaking ability, Moutinho was largely anonymous at White Hart Lane
Tottenham almost signed him a few years ago but he would struggle to make it into the home side's XI on this evidence.
WHO'S UP NEXT
Tottenham v Newcastle (Premier League, Sunday 13 December)
Monaco v Saint-Etienne (Ligue 1, Sunday 13 December)
Source : PA
Source: PA