But Toure put the visitors back in front with his 12th goal of the season and Kolarov got their third with an excellent solo goal.
Bony got his second in time added on to give Swansea hope, but City held on for a 3-2 win.
Their previous visits to Swansea had ended in a defeat and a draw but, after a difficult period either side of the break, they recovered to claim victory on this occasion.
City have now dropped points in just one of their past nine games and this three points moved them top of the table, at least until Arsenal face Cardiff later on.
The result continued the recent upturn in City's away form and Pellegrini was delighted by the grit his side showed after Bony had equalised, a goal the Chilean felt had been offside.
He said: "I think the most important part of the performance was to score the second and the third goal.
"After the offside goal, Swansea grew and they had a lot of chances in the second half and we knew that it would be very difficult for us. But the team, the same as in other games, had the character to change it."
He added: "That character is very important because at the beginning of the season we dropped too many points away.
"I think it's not good for this team to win just 11 points out of 27 in the first half of the season.
"Winning here, the first game away [in the new year], is very important for us.
"I think the key to the better away form was to continue playing exactly the same way we did at the beginning; we didn't lose the games against Cardiff and Aston Villa because we didn't play well. We made a lot of mistakes and conceded easy goals."
But Pellegrini remained coy on his side's title chances, despite extending their unbeaten run to nine games.
"We will try that is why it is important to win in any way you can," he said.
"We have difficult games away from home if we are to win the title, and difficult games at home as well. There are 18 difficult games and I am sure five or six teams will be fighting right to the end to try and win the title. The team that copes best will win it."
City are also understood to be considering playing a friendly in the United Arab Emirates against Al Ain on January 14, between Premier League fixtures against Newcastle and Cardiff, although an FA Cup replay could force the game to be scrapped or moved to a different date.