The Argentine international midfielder struck a first-half treble with three well taken goals to put us firmly in control at the interval and, while Stephan El Shaarawy scored a fine goal for Monaco midway through the second period, Carroll rounded off a great night with his landmark strike.
The victory meant we finished top of the table ahead of Monday’s draw for the Round of 32.
It was an excellent team performance which also saw a first start for 18-year-old midfielder Josh Onomah, who looked perfectly at home in the number 10 role, while Nabil Bentaleb and Nacer Chadli made their returns from injury with substitute appearances.
As well as Onomah, there were starts for the likes of Kevin Wimmer, Clinton Njie, Kieran Trippier, Ben Davies and Carroll as Mauricio Pochettino shuffled his pack during this busy spell of matches. Young centre-half Cameron Carter-Vickers, 17, was on the bench for the first time too.
We were quickly out of the blocks and ahead within two minutes. Davies won possession deep in Monaco’s half and found Clinton, who returned the favour with a pass down the left flank, allowing the full-back to break into the area and cut back for Lamela to stroke into the bottom corner.
It was comfortable for us in the opening stages as we dominated possession and opened up Monaco on a number of occasions. On 14 minutes, neat build-up play involving Carroll, Lamela and Onomah ended with Heung-Min Son blazing high over the bar. But just seconds later, Eric Dier won a header on half-way which Son flicked on into the path of Lamela and he was through on goal, the attacking midfielder hitting a low skidding drive from 22 yards which sneaked under goalkeeper Danijel Subasic and into the net.
Two minutes later, Lamela was bursting through again, this time just delaying his pass through to Son, who went on to convert the chance but the flag was up for off-side. Son then tried an acrobatic effort from a corner but hit the side netting.
It remained one-way traffic and another quick break on 24 minutes saw Onomah lead the charge, he rode a challenge before finding Clinton who poked the ball to Carroll, his 20-yard effort just clearing the crossbar. At the other end a free-kick was cleared as far as Tiemoue Bakayoko, whose drive was deflected away for a corner - the visitors’ first effort on goal in the 25th minute.
They had another sniff a few minutes later when Joao Moutinho’s free-kick was headed wide by Wallace, but we were soon back on the offensive when Onomah received a return pass from Lamela, broke into the area and tested Subasic at his near post.
The third goal duly arrived in the 37th minute and it was that man Lamela again, completing his hat-trick. Clinton nipped in to win the ball, Son sent a first-time pass to the midfielder who advanced into the area and drilled past Subasic at his near post.
We made a change just before the interval when Bentaleb came on in place of Dier, who appeared to pick up a slight knock. It was the Algeria international’s first appearance since sustaining an injury himself in our home game against Everton at the end of August.
It was a much quieter start to the second period, neither side creating anything of note until the 56th minute when good build-up play around the edge of the Monaco box saw Son slip a pass in to Onomah, he cut inside and only had Subasic to beat but his shot diverted off the goalkeeper for a corner.
The visitors got on the scoresheet just after the hour mark with a very well-taken goal from El Shaarawy. He received a pass from 16-year-old substitute Kylian Mbappe before curling a right-foot shot past Hugo Lloris and into the far corner.
Another returning player entered the fray in the 62nd minute when Chadli made his first appearance since being sidelined with injury seven weeks ago - the Belgian international going on for Lamela, who left the field to great applause following his treble.
It was Monaco who were having the better of the opportunities at that stage, Mbappe having an effort blocked and Nabil Dirar sending a header over the bar from the resulting corner as the visitors stepped up their efforts to reduce the deficit further.
But we almost added a fourth in the 73rd minute when we broke through Onomah and Davies, the Welsh full-back sliding a pass to Son. He was tackled on the edge of the area, Davies’ shot was blocked, the ball ran to Clinton who hit it first time but Subasic saved with his legs.
The keeper then did exactly the same five minutes later to deny Clinton again but this time the ball bounced out to Carroll, who controlled with his chest on the edge of the area to burst past two defenders. He then beat another to reach the byline before sliding the ball under Subasic and into the net from a tight angle, his first goal in our colours in his 32nd appearance, capping off a great night all round.
Spurs (4-2-3-1): Lloris, Trippier, Alderweireld, Wimmer, Davies, Carroll, Dier (Bentaleb 42), Lamela (Chadli 62), Onomah, Clinton (Alli 79), Son. Substitutes (not used): Vorm, Carter-Vickers, Townsend, Kane.
Monaco (4-3-3): Subasic, Dirar, Wallace, Toulalan, Elderson, Moutinho (Lemar 46), Bakayoko, Pasalic, Silva (Diarra 65), Traore (Mbappe 56), El Shaarawy. Substitutes (not used): Nardi, Carvalho, Mexique, N’Doram.
Goals: Spurs – Lamela 2, 15, 37, Carroll 78; Monaco – El Shaarawy 61.
Yellow cards: Spurs – Bentaleb; Monaco – Wallace, Toulalan, Dirar.
Referee: Ivan Bebek (Croatia).