Spurs came into the match with a slender 2-1 aggregate advantage having come from behind to triumph in Larnaca, but AEL provided nowhere near as stern a test this time around on Thursday.
First-leg goalscorer Harry Kane had a 13th-minute penalty saved by substitute goalkeeper Pulpo Romero, who was on the field after Karim Fegrouche took a heavy blow to the face in bringing down Kyle Naughton for the spot kick. But Kane did eventually break the deadlock in the 45th minute.
The impressive Paulinho set-up Kane and gave Spurs ample breathing space with a goal of his own in the 49th minute.
Andros Townsend pressed his claims for a place in coach Mauricio Pochettino's first-choice XI by converting a 66th-minute spot-kick as the former Southampton boss extended his perfect start in charge of the north London club to four matches.
Pochettino made five changes to the side that contested the first leg, while AEL were unchanged from the XI that took the lead in Cyprus.
In the sixth minute, Fegrouche tore out to clatter through Naughton on the left-hand corner of AEL's box, leaving referee Miroslav Zelinka with little option other than to point to the spot.
A seven-minute delay followed as Fegrouche received treatment for a nose injury and concussion, but Zelinka's leniency in only handing him a yellow card meant he was replaced by Romero, who saved with his feet as Kane's penalty lacked height.
Romero got the better of Kane once more after the Tottenham youngster drove at the visiting defence in the 19th minute.
Mousa Dembele dragged wide from the edge of the box as AEL offered precious little in terms of attacking threat, while Kane erred once more in the 37th minute, lifting over left-footed from Aaron Lennon's back-pass.
The England Under-21 striker was finally on target as the first half ticked down, slotting home after Paulinho pounced on a slack pass from AEL captain Marios Nikolaou.
Paulinho got himself of the scoresheet four minutes into the second half to put the tie beyond doubt.
Pochettino's trademark pressing style was in evidence as Spurs relentlessly harried their opponents, Vladimir Chiriches decisively dispossessing Diallo Guidileye on the edge of the area for the Brazil international to finish.
AEL's Carlitos got back to head Lennon’s instinctive chip wide as Paulinho again caused problems, before Townsend succeeded where Kane failed.
Edmar Silva handled Naughton's cross and Townsend - named in Roy Hodgson's England squad on Thursday despite failing to make Tottenham's matchday 18 against QPR last weekend - stroked coolly into the bottom corner as Romero went the wrong way.
Romero stopped Kane at close quarters in the 77th minute and turned away rasping drives from Townsend and Ben Davies as AEL flagged in the final stages.
By contrast, Tottenham brimmed with confidence and will be welcomed by few in Friday’s group-stage draw.