Fernando Amorebieta gave Toure a helping hand, conceding two penalties with rash challenges that earned the visiting defender a red card and allowed the Ivorian to put City 2-0 up.
He completed his treble with a magnificent third goal and further strikes from Fernandinho and Martin Demichelis sealed a win that took City to within six points of leaders Chelsea, with three games in hand.
Manuel Pellegrini’s side had made a slow start to the game at the Etihad Stadium, with the home crowd growing unsettled until Amorebieta gifted them the opening goal after 25 minutes.
There appeared little danger as Alvaro Negredo jumped to try and control a through ball on his chest, but the Fulham centre-back kicked the Spanish forward from behind and referee Jonathan Moss awarded a penalty.
Toure showed admirable poise, taking his time in approaching the ball before sending David Stockdale the wrong way for a 1-0 lead.
Amorebieta escaped with a yellow card on that occasion, but his afternoon came to an abrupt end in the 52nd minute when he made an impetuous tackle on David Silva and conceded a second penalty.
After the Venezuelan was shown a red card, Toure again made short work of the resulting penalty, beating Stockdale in almost identical fashion.
The hat-trick goal, comfortably the pick of the three, came from a short free-kick that Samir Nasri laid off for Toure to curl an unstoppable shot into the top corner from 25 yards.
Brazilian midfielder Fernandinho added a fourth six minutes from time when Fulham defended poorly at a City corner, enabling him to shrug aside William Kvist before scoring from a wide angle.
– City make slow start –
And there was time for defender Demichelis to tap into an open goal in the 88th minute after Stockdale had deflected Stevan Jovetic’s shot into his path.
The first penalty had been a timely opener, because last-placed Fulham were growing in confidence and had almost snatched a surprising opening goal just moments earlier.
Kieran Richardson wasted a free-kick with a shot directly into the City wall, but the home side failed to clear the danger and after Cauley Woodrow saw a shot blocked, Richardson connected with an 18-yard attempt that whistled just wide.
City, knocked out of the FA Cup and Champions League in the past fortnight, did not carve out a chance until Stockdale saved well from a crisp, first-time James Milner shot after 17 minutes.
Even after breaking the deadlock, City lacked control and might have conceded just after the half hour.
Steve Sidwell sent Richardson down the left and his cross was met at the far post by Sascha Riether, who should have done better than flick wide.
City finally strung together one of their trademark passing moves after 36 minutes, with Silva on the end of it, chipping over the goalkeeper, only for Amorebieta to head clear.
And just before the half-time whistle, Aleksandar Kolarov sped into the Fulham box and produced an angled drive that Stockdale did well to turn onto the Fulham crossbar at the expense of a corner.
The second penalty and dismissal, so early in the second half, effectively settled the outcome and Milner almost added a third goal on the hour when his clever footwork created room for a shot that just cleared the bar.
As City pressed on in an attempt to bolster their goal difference, Milner had a shot deflected just wide, Kolarov’s shot was parried by Stockdale and a Demichelis header was cleared off the line by John Heitinga.