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 satisfaction from a night which saw the likes of Harry Kane rested and fringe players step up.
Joshua Onomah, an 18-year-old academy product, 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.
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.
Pochettino’s men soon doubled their advantage as Lamela’s long shot skidded off the turf and underneath keeper Danijel Subasic.
The 23-year-old drove first time past Subasic to complete his quickfire treble after just 38 minutes.
El Shaaraway got one back but there was still time for Carroll to add a fourth.
Meanwhile Chelsea loanee Nathaniel Chalobah was among the scorers as Napoli advanced from their Europa League group with a 100% record following a 5-2 win over Legia Warsaw.
England U21 international Chalobah, who is yet to play a senior game for Jose Mourinho’s Blues, broke the deadlock in Naples before Lorenzo Insigne, Jose Callejon and Dries Mertens, who scored twice, got in on the act to make it six wins from six for the Italians.
They are the only club to progress without a dropping a point and they did so with a goal difference of +19 despite conceding goals to Stojan Vranjes and Aleksandar Prijovic.
Their qualification had already been sealed prior to kick-off and FC Midtjylland joined them in advancing out of Group D thanks to a 1-1 draw with Club Brugge, for whom ex-Middlesbrough forward Jelle Vossen scored.
Bordeaux and Rubin Kazan were knocked out having drawn 2-2 with each other in Group B.
It finished 1-1 in the Group A clash between Ajax and Molde too, a result that saw Molde finish top ahead of Fenerbache, who drew with Celtic.
Bruno Soriano’s stoppage-time equaliser ensured Villarreal finished top of Group E after a 3-3 draw with Viktoria Plzen. Rapid Vienna finish second despite a 2-1 win over Dinamo Minsk.
Borussia Dortmund go through as Group C runner-ups after a 1-0 home loss to PAOK, while Krasnodar’s 3-0 success at Gabala saw them top.
In Group F Marseille’s 4-2 win over Slovan Liberec saw them come second behind Sporting Braga, who were held to a 0-0 draw at Groningen.
Lloris, Trippier, Alderweireld, Wimmer, Davies, Dier (Bentaleb 42), Carroll, Onomah, N’Jie (Alli 79), Lamela (Chadli 62), Son.
Subasic, Wallace Santos, Toulalan, Echiejile, Bernardo Silva (Diarra 65), Pasalic, Bakayoko, Dirar, Lacina Traore (Mbappe 56), Joao Moutinho (Lemar 46), El Shaarawy.
Ivan Bebek (Croatia).
Anderlecht 2 Qarabag 1. Apoel Nicosia 1 Sparta Prague 3. Asteras Tripolis 0 Schalke 4. Atheltic Bilbao 2 AZ 2. Partizan 1 Augsburg 3. Dnipro 3 Rosenberg 0. St Etienne 1 Lazio 1. Skenderbeu 0 Lokomotiv Moscow 3. Sporting Lisbon 3 Besiktas 1. Fiorentina 1 Belenenses 0. Lech Poznan 0 Basel 1.