Marvin Sordell opened the scoring after just three minutes, with a deflected free-kick from Ross Wallace making it 2-0 just four minutes later.
We responded quickly, Paulinho pulling a goal back on 10 minutes, before Etienne Capoue levelled with a low drive in first half stoppage time.
Vlad Chiriches nudged us in front four minutes after the break, with Danny Rose completing the scoring three minutes later.
Teenage midfielder Josh Onomah then went on for his debut 15 minutes from the end.
Spurs: Vorm, Chiriches (Dier 80), Kaboul, Vertonghen, Davies, Stambouli, Capoue, Townsend (Onomah 76), Paulinho, Rose (Chadli 59), Soldado. Substitutes (not used): Lloris, Naughton, Dembele, Kane.
Burnley: Heaton, Trippier (Reid 68), Duff, Keane, Mee, Kightly, Arfield, Jones (Marney 76), Wallace (Boyd 89), Sordell, Vokes. Substitutes (not used): Gilks, Lafferty, Ings, Barnes.
Goals: Spurs – Paulinho 10, Capoue 47, Chiriches 49, Rose 52; Burnley – Sordell 3, Wallace 7.
Yellows: Burnley - Keane.
Referee: Craig Pawson.