Harry Kane fired us into the lead just before the half-hour mark while Ben Davies saw his effort come back off the crossbar in the second half, but Anderlecht got back on level terms when Imoh Ezekiel ghosted in to turn the ball home on 72 minutes.
We had the last laugh, though, as in-form midfielder Mousa Dembele unleashed a superb right-footed shot which sailed straight into the top corner with three minutes remaining to give us a 2-1 win - his third goal in as many games.
Spurs (4-2-3-1): Lloris, Trippier, Alderweireld, Vertonghen, Davies, Mason (Dembele 73), Dier, Lamela, Eriksen (Son 59), Alli (Onomah 77), Kane. Substitutes (not used): Vorm, Fazio, Wimmer, Carroll.
Anderlecht (4-2-3-1): Proto, Gillet, Mbodji, Deschacht, N’Sakala (Conte 83), Defour, Dendoncker, Najar, Tielemans (Ezekiel 69), Acheampong (Sylla 89), Okaka. Substitutes (not used): Roef, Suarez, Nuytinck, Dodi.
Goals: Spurs – Kane 29, Dembele 87; Anderlecht – Ezekiel 72.
Yellow cards: Anderlecht – N’Sakala.
Referee: Orel Grinfeld (Israel).