Toure fired in from 12 yards after Phil Jagielka was penalised for a challenge on James Milner, but the hosts were rocked by the early withdrawal of Sergio Aguero through injury.
Kevin Mirallas went close for the visitors, getting to a Pablo Zabaleta clearance first and volleying just off target care of a Fernando deflection, while Jose Angel Pozo almost made it 2-0 to City as he tested Tim Howard with a low effort.
Romelu Lukaku brought out a superb save from Joe Hart late on but the visitors could not make the most of plenty of second-half possession, and City held on to make the most of Chelsea’s earlier defeat at Newcastle.
Manuel Pellegrini made three changes from the midweek win at Sunderland, with Eliaquim Mangala returning from suspension, while Milner and Fernando came into the midfield.
Everton, meanwhile, lined up with Seamus Coleman on the right of midfield as Tony Hibbert came in at full-back. Roberto Martinez left Ross Barkley on the bench, with Samuel Eto’o supporting Lukaku up front.
The night started on a very sour note for the hosts who had to play most of the match without in-form striker Aguero, who limped off with what looked like a knee injury sustained as he stretched for a challenge.
It killed a good pre-match atmosphere and City struggled to get the crowd going as both sides endured a sloppy opening spell.
City broke the deadlock inside 25 minutes, though, as Toure slid a pass through for Milner and the midfielder got a touch on the ball before Jagielka came across to make a challenge. Referee Andre Marriner pointed to the spot straight away and Toure coolly slotted the penalty into the bottom corner.
The second half proved a much more open affair as youngster Pozo – who replaced Aguero – was denied low by Howard after excellent work by Milner out wide.
Martinez soon introduced Barkley to the action, and the change seemed to spur the visitors on as they enjoyed much more time on the ball.
Lukaku almost equalised with a wonderful effort as he latched on to Eto’o’s flick, but Hart produced a stunning stop to keep it out.
City had some chances of their own as the excellent Milner volleyed over after good work from substitutes Frank Lampard and Edin Dzeko, while Samir Nasri fired straight at Howard.
JAMIE REDKNAPP’S VERDICT
“When you put it into context – you lose your star striker after two minutes, you’ve got no Vincent Kompany, no David Silva – it’s a huge result. That’s so important, especially after what happened with Chelsea earlier. Those three points are vital. They weren’t at their best, but with those games you just need to win, to get across the line, and that’s what Manuel Pellegrini will be so pleased about.”
Manchester City: Hart (7); Zabaleta (7), Demichelis (7), Mangala (5), Clichy (7); Fernando (6), Toure (7); Jesus Navas (6), Milner (9), Nasri (8); Aguero (5).
Used subs: Dzeko (6), Lampard (7), Pozo (6).
Everton: Howard (7); Hibbert (6), Jagielka (7), Distin (7), Baines (6); Coleman (5), Barry (4), Besic (6), Mirallas (6); Lukaku (6), Eto’o (7).
Used subs: Barkley (6), Osman (6).
Man of the Match: James Milner