Harry Kane made amends for missing an early penalty when he fired home shortly before the break to give us a 1-0 lead on the night and put us 3-1 up on aggregate.
Paulinho then found the net shortly after the break, with Andros Townsend rounding off the scoring from the spot.
Spurs (4-2-3-1): Lloris, Naughton, Kaboul, Chiriches (Veljkovic 86), Davies, Sandro (Holtby 77), Dembele, Lennon, Paulinho, Townsend, Kane. Substitutes (not used): Friedel, Rose, Dier, Chadli, Adebayor.
AEL (4-2-3-1): Fegrouch (Romero 12), Edmar, Sielis, Cadu, Carlitos, Nikolaou (Danielzinho 46), Guidileye, Bebe, Barcelos, Sardinero (Tagbajumi 80), Gikiewicz. Substitutes (not used): Romero, Espana, Carlitos, Eleftheriou, Nadeau.
Goals: Spurs – Kane 45, Paulinho 49, Townsend (pen) 66.
Yellow cards: AEL – Fergouch, Bebe.
Referee: Miroslav Zelinka (Czech Rep).