A first-half penalty from the Ivorian midfielder was enough to separate the two teams, but City's victory was overshadowed by the injury sustained by Sergio Aguero.
The club's top scorer handed the Citizens a blow when he left the stage early with the game just six minutes old with a knee injury.
Aguero was in tears as he departed the pitch and he was replaced by 18-year-old Jose Pozo.
City drew first blood when they were awarded a spot kick in the 24th minute.
James Milner tumbled in the area under the challenge of Phil Jagielka and Toure rolled the ball calmly into the bottom corner of the net.
PA
Sergio Aguero in tears after coming off with a knee injury
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
Toure gave City an injury scare when he went down clutching his leg but managed to shake it off and continued.
City exerted more pressure in the second half and should have doubled their lead when Pozo drilled a shot from 10 yards, but Tim Howard repelled the effort with his feet.
Everton nearly snatched an equaliser 10 minutes from time when Romelu Lukaku fired a volley goal wards, but Joe Hart stuck out a strong hand to thwart him.
City are just three points adrift of table toppers Chelsea, who lost 2-1 away to Newcastle earlier in the day.