The hosts took the lead 16 minutes into the match at Brisbane Road when Adam Smith handled Scott McGleish's shot on the goal-line and Ben Chorley scored from the resulting penalty kick.
McGleish doubled Orients lead just moments after.
Ryan Mason reduced the deficit 10 minutes into the second half slotting home from a right wing cross by Jonathan Obika.
Obika himself equalised for Spurs when he headed home from Nathan Byrne cross 15 minutes from time.
Orient: Jones (Butcher, 62); Omozusi, Chorley (Tozer, 46), Forbes (Brown, 62), Cestor (Eagle, 59); Chambers (Smith, 46), Dawson, Spring, Cox; McGleish (Tehoue, 46), Revell (Jarvis, 62).
Spurs XI: Button (Jansson, 46); Smith (Nicholson, 89), Butcher, Byrne, Rose (Durojaiye, 46); Fredericks (Kane, 56), Dawkins, Mason, Townsend (M'poku,46); Taarabt (Parrett, 46); Obika.