The former Chelsea trainee made it six goals in seven games to help the Irons consolidate their position in the top half of the table.
Italian David Di Michele put the home side ahead in the first half, after Mark Noble’s penalty was earlier saved by inspired Hull keeper Matt Duke. New signing Savio Nsereko came off the bench for the final few minutes, but by then the job was done.
For Tigers boss Phil Brown — who gave £5m midfielder Jimmy Bullard a debut in the second half — his work goes on to ensure a fine opening to the campaign does not end in disaster.
The match burst into life on 15 minutes. Noble’s shot was deflected behind for a corner, which eventually dropped out to Jack Collison and his low strike was well saved a full stretch by Duke.
The Hull keeper was left a spectator moments later when Di Michele unleashed a superb curling effort from outside the box which came back off the inside of the far post. The Hammers were awarded a penalty, in the 21st minute, when Sam Ricketts was adjudged to have bundled over Cole as the pair tussled in the six-yard box.
Noble drilled the ball towards the left corner, only for Duke to pull off a stunning save at full stretch.
Duke made another acrobatic save – but this time could only push the ball out and it dropped right into the path of Di Michele at the far post, who smashed the Hammers ahead on 34 minutes.
Cole should have made it 2-0 just before the break when he raced clear but Duke made another fine block.
Hull fell further behind on 51 minutes. A deep free-kick by Noble dropped at the far post for Di Michele. His low strike bounced off the foot of the upright and into the path of Cole, who diverted it to the roof of the net.
To their credit, Hull continued to try to take the game to the hosts. However, West Ham found more space as the match went on, with Cole and Di Michele both having efforts blocked.
Duke touched a chipped effort from Noble over the bar, with the Hull keeper making another fine save from Julien Faubert before Savio was handed a cameo for the final four minutes.
WEST HAM: Green, Neill, Collins, Upson, Ilunga, Behrami, Parker, Collison (Faubert 71), Noble (Boa Morte 84), Di Michele (Nsereko 86), Cole.
HULL: Duke, Ricketts, Turner, Zayatte, Dawson, Marney (Mendy 73), Ashbee, Kilbane, Geovanni (Bullard 53), Cousin, Manucho (Fagan 53).
Referee: H Webb (S Yorkshire).