Harry Kane headed us into the lead on 21 minutes, but Ashley Barnes hit a spectacular equaliser six minutes later.
The winner came from Erik Lamela, who curled into the net from outside the box nine minutes before the break.
Spurs: Lloris, Walker, Vertonghen, Fazio, Davies, Mason (Stambouli 44), Bentaleb, Lamela, Eriksen (Rose 90+3), Chadli, Kane (Soldado 84). Substitutes (not used): Vorm, Chiriches, Dembele, Townsend.
Burnley: Heaton, Trippier, Shackell, Keane, Mee, Arfield (Wallace 79), Marney, Jones, Boyd (Kightly 79), Barnes (Jutkiewicz 89), Ings. Substitutes (not used): Gilks, Reid, Chalobah, Long.
Goals: Spurs – Kane 21, Lamela 36; Burnley – Barnes 27.
Yellow cards: Spurs – Davies.
Referee: Mike Jones.