A Robbie Brady penalty after only 12 minutes was enough to secure a second victory on the bounce for the Tigers over an under-performing Hammers side.
The Hammers will go away feeling hard done by after having a penalty appeal themselves turned down by referee Kevin Friend when he failed to spot a handball from on-loan Spurs man Jake Livermore with only 10 minutes left on the clock.
The Hammers pressurised the hosts towards the end but were unable to find a way past Alan McGregor in the Hull City goal.