Roberto Mancini's defending champions are 13 points adrift of their cross-city rivals with five games left to play for both sides.
Yet for the majority of the match it seemed as though City would clinch a routine win and keep their slim hopes of retaining the title alive after Nasri steered in James Milner's pullback.
Tottenham went into the match on the back of a 10-day break following
their Europa League exit at Basel
but they produced a lethargic display until bursting into life after Dempsey's equaliser.
Up to that point, City's assurance in possession, coupled with their willingness to drive forward on the counter-attack, served to frustrate the majority inside a subdued White Hart Lane.
Man Utd deserve title win - Mancini
The visitors spurned several chances to double their lead as Nasri poked wide from Carlos Tevez's ingenious flick and Spurs keeper Hugo Lloris stopped the Argentine striker's header with an instinctive one-handed save.
But Dempsey, clearly on-side despite the protest of the City defence, pounced at the far post to convert Bale's outside-of-the-boot cross and punish their profligacy.
Suddenly, the home crowd found their voices and the players found their belief as they upped the tempo in search of the lead.
It came four minutes later when substitute Defoe, who had only just entered the action as a replacement for the ineffective Emmanuel Adebayor, cut inside City skipper Vincent Kompany before unleashing a unstoppable angled drive past Hart.
Tottenham talisman Gareth Bale has been involved in 12 goals in his last nine Premier League appearances. The Welshman has scored nine times and provided three assists.
Spurs looked a completely different team as their energy levels rose, in contrast to a City team who started to look like they were feeling the effects, both mentally and physically, of a hectic week.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.