Cypriot outfit AEL looked set to inflict a shock defeat on Mauricio Pochettino's side, as Adrian Sardinero fired them into an early lead, but Erik Lamela’s game-changing introduction in hot and humid conditions altered the course of the tie as he assisted second-half replies from Roberto Soldado and Harry Kane.
It is fair to say neither club nor player will have been pleased with the way things have gone since Lamela arrived at White Hart Lane last summer in a club-record £30million deal.
The Argentine forward managed just three league starts for Spurs in an injury-disrupted debut season but at last he is showing signs of promise, with his introduction here the catalyst to Tottenham's victory.
It had looked for a long while like Pochettino would rue his decision to leave Emmanuel Adebayor, Christian Eriksen, Younes Kaboul, Aaron Lennon and Etienne Capoue at home.
He chose to make seven changes from the side that won 1-0 at West Ham United, including giving summer signing Ben Davies his debut and the late-returning World Cup duo of Jan Vertonghen and Paulinho their first run-out of the campaign.
This was seen as a good opportunity to get the pair back in action, but their rustiness was ruthlessly exposed inside 14 minutes.
The duo were involved as Spurs inexplicably gave up possession in their own half, with Sardinero taking full advantage by racing through to shoot low past Hugo Lloris.
It was a fine finish from the Spaniard but one completely against the run of play, given Spurs had not only bossed possession up until that point but had chances as well.
Soldado should have given Spurs the lead after five minutes, only to shoot horribly wide from close range, albeit off-balance, after Karim Fegrouch parried a Kane strike into his path.
Paulinho also missed the target and Kane struck a 30-yard free-kick just over before Sardinero's opener, which left Spurs visibly shell-shocked.
A Soldado handball appeal and hopeful long-range Kane effort was all Pochettino's men were able to muster until the impressive 21-year-old forced a wonderful save from Fegrouch.
AEL were looking a far more confident outfit than the one that began the game, though, and could have doubled their advantage had Lloris not darted off his line to smother a Sardinero effort.
Vertonghen produced a great block to stop Diego Barcelos getting a shot away from the edge of the box before the whistle brought an end to an under-par Spurs display.
Things continued shakily, though, and once Vertonghen blocked another Barcelos effort, the home crowd were angered by the referee waving away calls for handball against Eric Dier.
Carlitos hit the side-netting with a low drive after neat play down the right as Spurs continued to struggle, leading Pochettino to replace the ineffective Paulinho with Nacer Chadli as the match entered the final half an hour.
AEL were having to defend resolutely to thwart Tottenham, who came agonisingly close to levelling in the 71st minute when Kane hit the under-side of the bar from a Soldado knock-back.
Lamela was introduced moments later and made the ideal impact, setting up the equaliser less than two minutes after coming on.
The Argentinian floated a wonderful ball to the edge of the box for Soldado, who struck home a first-time effort in front of the visiting support.
It was a fine goal and one which was followed-up six minutes later by another. Lamela was again the architect, playing through Kane to strike into the top left-hand corner.
Things could have got better still for the 22-year-old, directing a Kyle Naughton cross just wide before being denied by the AEL goalkeeper towards the end of a game which could be the making of him.