The Canaries spent much of the game on the front foot at Carrow Road but failed to take advantage of the chances they created as the two sides shared the spoils
The Canaries edged the encounter on chances created but failed to take advantage of the opportunities they carved out, with their best spell coming in the lead-up to halftime.
As the match wore on Norwich's pressure faded but West Ham could not grab a winning goal of its own despite the positive impression made by substitute Matthew Jarvis.
Hughton's team has now drawn three consecutive matches and has turned in respectable performances in all three but are still yet to touch the win column.
With Andy Carroll injured, Carlton Cole led the line for West Ham and was flanked by Ricardo Vaz Te and Matthew Taylor. Norwich made only one change to the team that drew against Tottenham at White Hart Lane, introducing Andrew Surman on the left side of midfield in place of Anthony Pilkington.
Surman was close to making an immediate impact. After good work from Grant Holt on the wing the former Southampton midfielder stepped past James Collins before firing narrowly wide across goal from a tight angle.
West Ham was largely placed on the back foot but while it did not venture forward too often, it tended to create a quality chance to score every time they did. Cole had a header cleared off the line by Russell Martin before John Ruddy did well to deny Kevin Nolan from a similarly central position in the penalty area.
Sam Allardyce's team had only itself to blame for the errors it made in its last away game, against Swansea City, that led to a comprehensive 3-0 defeat and calamitous defending from Joey O'Brien almost gifted Norwich the lead after 28 minutes. The left back's clumsy control near the touchline allowed Robert Snodgrass to nip in but the winger failed to pick out Simeon Jackson, who was waiting in the penalty area.
Snodgrass was at the center of things again when West Ham's failure to clear its lines led to a remarkable sequence of four chances in quick succession, but Jussi Jaaskelainen stood firm to make three saves and Sebastian Bassong headed the final opportunity over the crossbar.
The first half ended on a controversial note when Surman, making another excellent darting run, was hacked down by Collins around the edge of the box. The Canaries players furiously appealed for a penalty but referee Chris Foy was entirely correct in awarding a free kick just outside the area.
After Jackson and Snodgrass had both shot narrowly off-target from distance early in the second half, Allardyce decided that he had seen enough and threw Jarvis and Modibo Maiga into the fray in place of the ineffective Cole and Taylor. The away side improved thereafter and one trademark Jarvis cross dipped just beyond Vaz Te at the far post.
Norwich struggled to create chances in the closing stages as its midfield tired but substitute Harry Kane wasted a golden chance to secure the points when he weakly shot at Jaaskelainen at the end of a three-on-two counter-attack.
The crowd's frustration only increased as full time drew closer and Norwich now face a daunting run of fixtures against Newcastle United, Liverpool, Chelsea and Arsenal as its continue their search for three points.
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