The east London side went into the clash having already won at the Emirates Stadium, Etihad and Anfield this season.
But Slaven Bilic's men were clearly hungry for yet more success and, following a Nemanja Matic sending off and some Jose Mourinho & Kurt Zouma drama, duly got their reward.
And former West Ham midfielder Sinclair took to Twitter after Carroll's winner, calling the 26-year-old an 'aerial bully.'
Been saying hang 1 up there for 5 mins ????? 2-1 Andy Carroll is an Ariel bully #coyi— Trevor Sinclair (@trevor8sinclair) October 24, 2015
He told BBC Football: "That's why Andy Carroll is in the team! Chelsea had a chance to clear it moments before but the ball came into the box and they have been punished for not doing so. When Carroll is 100% fit he is incredibly difficult to handle."
It looks as though those who backed Carroll when he was out injured were proven right, then.
In the air, there is no one better, while West Ham's strength in depth now looks frightening. There is no reason they can't remain at the right end of the table for the rest of the season.