Burnley climbed off the foot of the standings by recording its first away triumph, with Danny Ings' double claiming a 2-1 victory at Stoke.
West Ham's five-match unbeaten run ended with a 2-1 loss to Everton, while Leicester's goalless run went beyond 500 minutes after drawing 0-0 with Sunderland.
Scoring is no problem for Chelsea. Costa volleyed in the opener in the 11th minute at Stamford Bridge after meeting Oscar's cross. Cesc Fabregas, the instigator of so many goals since joining Chelsea this season, whipped in the corner that Hazard scored from in the 25th.
The only surprise for Chelsea was the failure to record a more impressive victory margin after Claudio Yacob saw red for a challenge on Costa in the 29th.
"They knew that the points were not at risk," Mourinho said. "The objective was to win the three points and I think they also knew that, because we spoke about it at halftime, that the first half was absolutely beautiful. Many, many times I am upset, but I think not today."
Neither was Manchester City manager Manuel Pellegrini thanks to the champions' comeback, having raised the tempo after falling behind.
Bony skillfully put Swansea in front, using his chest to control Nathan Dyer's ball before sending the shot past goalkeeper Joe Hart in the 9th. But Jovetic leveled 10 minutes later, diverting Jesus Navas' cross past goalkeeper Lukasz Fabianski.
City equalised when Toure pushed forward and fed Jesus Navas out wide. The Spaniard curled an inviting low ball into the area and Jovetic stuck out a leg to divert past Lukasz Fabianski.
And Toure scored just his second league goal of the season in the 62nd after combining with Fernandinho.
"It is impossible for Yaya to score again the amount of goals (20) he scored last season," Pellegrini said. "That was not normal. He is not a striker, he is a midfielder. But it is important for him to score the way he did."
-AP