Harry Kane missed an early penalty for Spurs but Mauricio Pochettino's men made light work of their Cypriot opposition at White Hart Lane
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.
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.
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.
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 in the second half to put the tie beyond doubt.MORE: Alex Morgan upset at 159-degree temps | Transfer photos
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.
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.