Sunderland's Max Stryjek was the busier of the two goalkeepers.
He denied Shayon Harrison early on before making a double save from Anthony Georgiou (pictured) in the 76th minute.
Spurs remain bottom of the table - one point behind the Black Cats and two behind 10th-placed Manchester United.
Spurs: 3 Jan v Leicester (A) PL2
Sunderland: 7 Jan v Derby (H) PL2