Kevin Keegan left looking on with a sense of disbelief as his side again failed to see a match through after taking the lead.
Nicolas Anelka put City ahead in this FA Cup tie but a mistake by goalkeeper Kevin Ellegaard allowed Gary Doherty to equalise.
It means the teams will reconvene at White Hart Lane a week on Wednesday for a fourth-round replay.
City boss Keegan must be concerned at the fragile confidence of his side after a dreadful run that has seen them win only one of their last 17 games.
Robbie Fowler returned to the City team after recovering from a knee problem.
He partnered Nicolas Anelka up front with Jon Macken having to settle for a place on the bench.
Antoine Sibierski was again preferred to Steve McManaman while goalkeeper Ellegaard replaced the cup-tied David James.
With Gus Poyet suspended, former City midfielder Michael Brown retained his place in the Tottenham team on his 27th birthday.
Sibierski found space on the left in the first minute but his tame shot did not trouble goalkeeper Kasey Keller.
Then Brown tried to pick out Robbie Keane only for Ellegaard to race off his line and gather safely.
Keller had to look alert to turn away a shot from Fowler in the 10th minute - but a minute later City took the lead.
Michael Tarnat swung in a corner from the left that was headed away by Tottenham defender Gary Doherty.
City skipper Sylvain Distin knocked the ball back in and Fowler saw his header come back off the post.
Nicolas Anelka was on hand to force home the rebound for his 18th goal of the season.
It was just the start City wanted after one win in the last 16 games and that was in the last round against Leicester.
Fowler sprung the offside trap in the 26th minute after Sinclair flicked the ball on but his touch let him down.
There was another scare for Tottenham in the 29th minute when Richard Dunne got on the end of Tarnat's free-kick only to head marginally wide.
Then a careless back pass from Ledley King saw Anelka scamper clear on goal.
However, Mauricio Taricco managed to get back and do a sound mopping up job to the relief of his team-mate.
Ellegaard was called into action for the first time in the 37th minute and reacted superbly to parry Simon Davies' 20-yard effort.
Claudio Reyna should have added a second goal for City in the 40th minute when he was released by Sun Jihai.
Keller had vacated his goal but Reyna was unable to take advantage, hooking wide from a good position.
Tottenham manager David Pleat made a couple of changes at half time in a bid to turn the match around.
Stephane Dalmat and John Jackson came on for Darren Anderton and Tarrico, who was still suffering from that knock early in the game.
Tottenham were first to show in the second half when Keane burst through but Ellegaard was equal to his effort from an acute angle.
Play switched up the other end and Keller was forced to make a hasty clearance after Anelka got the better of Doherty.
Keane then released Helder Postiga but his touch was so poor the ball ended in the arms of Ellegaard.
Tottenham equalised in the 57th minute after a mistake by Ellegaard, who had been given the nod ahead of Iceland number one Arni Arason.
Ellegaard failed to meet a corner from Postiga, which looped over him, and Doherty headed in unchallenged at the far post.
There almost an action replay a minute later but this time Doherty's effort cleared the bar.
City were suddenly under siege and Postiga got ahead of Ellegaard when Anthony Gardner knocked the ball in only to find the wrong side of the post.
Then Brown thumped in a free-kick from the edge of the area that City's young 'keeper did well to parry.
City pushed forward in an effort to get back in the game and Tarnat released Sinclair but his shot went over the bar.
The Paul Bosvelt got into a good position but found the arms of Keller with his effort.
Postiga should have put Tottenham ahead but somehow from three yards managed to a send a free header from Keane's cross over the top.
Then it was sub Jon Macken's turn to be wasteful for City when he knocked a shot wide with only Keller to beat.
Teams
Man City Stuhr-Ellegaard, Jihai, Dunne, Distin, Sinclair,
Reyna, Bosvelt, Sibierski (Wright-Phillips 69), Tarnat, Anelka,
Fowler (Macken 69).
Subs Not Used: Arason, McManaman, Sommeil.
Booked: Reyna, Bosvelt.
Goals: Anelka 11.
Tottenham Keller, Carr, Doherty, Gardner,
Taricco (Jackson 45), Anderton (Dalmat 45), Brown, King,
Davies, Postiga, Keane.
Subs Not Used: Hirschfeld, Bunjevcevic, Zamora.
Booked: Anderton, Carr.
Goals: Doherty 57.
Att: 34,000
Ref: S Dunn (Gloucestershire).
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