Ruben Lameiras was denied by Foxes stopper John Maddison and then the crossbar, while Emmanuel Sonupe also hit the frame of the goal before the interval.
Both defences stood firm in the second half, however, and the points were shared.
Spurs: Archer, McQueen, Walker-Peters, Ward (Lesniak 85), Ogilvie, Khumalo, Sonupe, Winks (Miller 78), Lameiras (Akindayini 66), Onomah, Oduwa. Substitute (not used): Miles (GK).
Leicester City: Maddison, Pearson, Chilwell, Sesay (Choudhury 46), Moore, Upson, Dodoo, McCourt, Stankevicius, Panayiotou, Fox. Substitutes (not used): Davies, Rowe, Ndukwu, Smith-Varnham (GK).