Manchester City were made to rue missed chances on a frustrating afternoon, as they were punished by a clinical Chelsea side.
The home side dominated the first 45 minutes and had a couple of penalty appeals turned down by referee Anthony Taylor.
Gary Cahill handled the ball with a trailing hand after he was cut up by David Silva, but it wasn't deemed deliberate by Taylor. City were then left aggrieved when David Luiz blocked Aguero's run through on goal, which would have seen him go one-on-one with Courtois, but no free-kick was given, although replays show that it probably should have been a free-kick and maybe even a red card for the Chelsea defender.
The home side then had a final penalty appeal turned down for a challenge on De Bruyne by Kante, but once again shouts were turned away.
City did manage to take the lead on the stroke of half-time when Gary Cahill put Jesus Navas' cross past his own 'keeper.
City continued to dominate after the break, and had the perfect chance to double their lead after the break when Navas played the perfect pass for Kevin De Bruyne at the back post, but the Belgian somehow managed to hit the crossbar from point blank range.
Chelsea then scored a goal against the run of play on the hour. Cesc Fabregas, making his first start since September, played a good pass over the top for the Chelsea striker, who took the ball on his chest, cut inside and fired a low shot past Bravo.
10 minutes later and Chelsea went ahead thanks to substitute Willian. Chelsea hit City on the break, with Costa feeding in Willian and he hit his effort past Claudio Bravo who could have perhaps done more to prevent the away side taking the lead.
Guardiola's side were then punished again on the counter-attack on 90 minutes as they pushed forward in search of an equaliser. Alonso played an exquisite pass for Hazard who went through on goal and sealed the win for Conte's men.
However, there was still time for late drama as Aguero and Fenandinho were both sent off in the seventh minute of stoppage time. The former overran the ball and caught David Luiz with a crazy, high lunge which caused a mass brawl between City and angered Chelsea players.
Fernandinho then took a disliking to Cesc Fabregas, grabbing him around the neck before pushing him over the advertising hoardings, seeing red for his actions.
Victory for Chelsea means that Conte's men move four points clear at the top of the Premier League, having won eight games in a row.