Sven-Goran Eriksson's City, who had won only twice in their last 12 Premier League matches, were forced to come from behind to end a barren run of results.
Robbie Keane fired Spurs ahead with his 23rd goal of the season, only for City to hit back with second-half efforts from Stephen Ireland and a first-ever senior goal from defender Nedum Onuoha.
This helped City improve their dismal home record as Spurs had only lost once in their last 14 visits since 1994.
Spurs had looked set to extend that impressive run of results until they ran out of steam in the second period.
That was undoubtedly due to their UEFA Cup match in Holland on Thursday against PSV Eindhoven which had gone to a penalty shoot-out after two hours of football.
City were unlucky not to take the lead midway through the opening half when they were twice denied within the space of seconds, each time by defender Michael Dawson.
First he blocked Michael Johnson's goalbound shot and then he chested Elano's shot off the line after keeper Paul Robinson had been beaten.
Spurs made the most of their good fortune to take a 32nd minute lead when Vedran Corluka's error let in Pascal Chimbonda, whose delicate pass released Robbie Keane and he fired home an exquisite shot from a tight angle.
City were unfortunate again late in the half when Johnson was denied by a last-ditch tackle from Chimbonda and the ball was only cleared to Elano, whose angled shot was well-beaten out by Robinson.
But just short of the hour, City's luck turned as they equalised through Ireland's third goal of the season.
Benjani Mwaruwari provided a far-post cross from the left, Nery Castillo mis-hit his shot which fell invitingly for Elano who headed into the path of Ireland and he squeezed home a shot from six yards.
And there was further joy for City who took the lead in the 72nd minute through a powerful header from Onuoha following a right-wing corner from Elano.
Spurs, whose captain Keane reacted angrily to being replaced by Darren Bent midway through the second half, staged a late onslaught in search of an equaliser.
Bent had the ball in the net from substitute Jamie O'Hara's free-kick only for the effort to be ruled out when a team-mate had strayed offside.
And City keeper Joe Hart also made hard work of saving from Dimitar Berbatov as they lived dangerously on several occasions.