Harry Redknapp's side huffed and puffed throughout the afternoon but could not find a way to break down a spirited Sunderland team, who spent most of the afternoon with nine men behind the ball while playing on the counter attack.
Rafael van der Vaart might well have won it for the visitors on 73 minutes when he dashed onto a pass from Luka Modric to lift the ball over home goalkeeper Simon Mignolet, but Michael Turner was ideally positioned to clear off the line.
Van der Vaart appealed for a penalty against Turner who seemed to accidentally handle, but referee Chris Foy decided it was not a penalty.
Spurs are one point clear of fourth-placed London rivals Arsenal, who need at least a draw against title-chasing Manchester City at home on Sunday to regain third spot in the standings on goal difference.
The race for the two Champions League qualification spots is heating up with only six points splitting Spurs, Arsenal, Newcastle and Chelsea, who will move alongside Newcastle on 56 points and within three points of Spurs if they beat Wigan later on Saturday.
Tottenham failed to score for a third Premier League away match in a row for the first time in five years. They remain without a league away victory in 2012, but at least tried to claim the three points with Louis Saha and Jermain Defoe thrown on late in the match.
Referee Foy could have awarded a penalty at either end in the first period with Phil Bardsley appearing to handle an Emmanuel Adebayor header on 13 minutes and Scott Parker nudging the ball with his hand on 32 minutes, but Foy probably called it right by deciding ball had played man.
Elsewhere in an eminently forgettable match, Benoit Assou-Ekotto dragged a shot wide for the visitors on four minutes with Gareth Bale nodding over from 12 yards out from an Assou-Ekotto cross on 58 minutes.
Kyle Walker managed to dart back to prevent James McClean from tapping Sebastian Larsson's cross into an open goal around the hour mark, but that was about it for the day.
Sunderland manager Martin O'Neill did not look too displeased with the draw as his side moved above Liverpool on goal difference in the table. They are up to eighth place, a point behind seventh-placed Everton.