Jose Mourinho and Nemanja Matic were sent-off as Chelsea's miserable Premier League campaign continued with a 2-1 defeat at West Ham on Saturday.
Mourinho was sent to the stands after an incident with the match officials in the tunnel at half-time, shortly after Matic had been shown a second yellow card.
At that point Chelsea were behind due to Mauro Zarate's 17th-minute opener, while Kurt Zouma had seen his header cleared off the line by Manuel Lanzini.
Despite playing with 10 men and Mourinho in the stand, Chelsea equalised though Gary Cahill but they could not hold on and Andy Carroll nodded home a 79th-minute winner for Slaven Bilic's high-flying side.
Payet's delivery from the resultant set-piece was not cleared effectively by Costa and Zarate took full advantage, drilling a first-time shot into the back of the net from the edge of the area.
Chelsea dominated possession but struggled to create goalscoring opportunities, with Adrian not called upon until the 33rd minute when he had to parry Willian's free-kick away from the bottom corner.
The Argentine nearly added to Chelsea's misery six minutes before the interval but, following a clever flick-on from Payet, his chip floated over the top.
The game did swing further away from Chelsea in the 44th minute, however, when Matic received a second yellow card for hauling Diafra Sakho to the ground, while John Terry and Fabregas were booked for their protests and goalkeeping coach Silvino Lauro was dismissed from the dugout by referee Jon Moss.
But he will have been cheered 11 minutes after the restart as his side equalised. Willian's corner fell kindly for Cahill, who pounced first to rifle the ball beyond Adrian and into the back of the net.
But in the 79th minute substitute Carroll – who replaced Zarate – looped a header beyond Begovic from Aaron Cresswell's lofted delivery from the left.
The victory was just West Ham's second in five home games this term, while Chelsea's troublesome start continues.
