It was not a happy evening for the visiting Canaries, who had two players sent-off in a minute of madness midway through the second-half.
On a chilly night in Dagenham the match started evenly with the Hammers playing some neat attacking football without breaking through the Norwich defence.
It was the visitors who had the first real chance of the evening when Adam Gusterson swung over a cross that dipped onto the top of Jimmy Walker's crossbar before bouncing away to safety.
The scare seemed to shake West Ham into life, and within a minute Kevin Keen's men had taken the lead. Mark Noble's slide-rule pass released Moses Ashikodi down the right. The Hammers striker beat Rossi Jarvis for pace and drilled a low cross into the box, where Youssef Sofiane was waiting to slot home from close range.
West Ham enjoyed much of the possession after taking the lead, but couldn't convert that dominance into chances as Norwich worked hard to deny them space. The visitors might have equalised just before half-time when a free-kick was whipped into the Hammers box, and the ball bounced awkwardly in front of Walker. But the West Ham 'keeper did well to gather under pressure from the Norwich forwards.
HT: 1-0
The second-half started much the same as the first, with neither side able to take control of the game despite the quick tempo of the match. The Hammers midfield, patrolled by the excellent Mark Noble who was captain for the night, played the ball around nicely, but it wasn't until a dramatic 68th minute that the game really came to life.
Moses Ashikodi burst through the Norwich back line and was bearing down on goal when he was tripped by Canaries centre-back Jason Shackell. A predictable red card soon followed. Noble bent the resulting free-kick around the Norwich wall only to see his dipping shot palmed away by Norwich goalkeeper Paul Gallacher.
With the placid game suddenly heating up, it was less than a minute before referee McDermid was brandishing the red card again. Gusterson's heavy challenge on Kyel Reid earned the Norwich full-back a second yellow card and at the end of an action-packed minute the Canaries were suddenly down to nine men.
Kevin Keen's Hammers took full advantage. Moses Ashikodi charged into the penalty area and was chopped down by Rossi Jarvis. The referee had no hesitation in pointing to the spot. Ashikodi picked himself up and coolly converted the penalty to put the Hammers 2-0 up.
Chris Cohen was involved in two goal line clearances, one at each end, as the final whistle approached. First he repelled Danny Crow's drive, before seeing his own goal bound shot headed clear with Paul Gallacher beaten. At the final whistle West Ham United could celebrate a well-deserved 2-0 victory.
Coach Kevin Keen said: "We put in a very good all round performance tonight. At the back we were really solid and limited them to just one real chance in the second-half.
"Our solid defence gave us the base to build going forward. Moses Ashikodi did really well for the first goal to set up Youssef Sofiane, and then he won and converted the penalty in the second-half.
"When Norwich had two men sent-off we kept our discipline really well, and overall I thought it was a well-earned three points."
WHU: Walker; McClenahan (Henry 46), Blewitt, Ward, Melville, Cohen, Noble, Wright (Stokes 73), Ashikodi (Allen 83), Sofiane, Reed. Subs unused: Behcet (GK), Laws.