Overall, it was a fairly mediocre contest as the Hammers put in an assured defensive display to deny the Canaries who had plenty of opportunities to come away with maximum points.
There was no shortage of endeavour from the players on a lovely day for football but the match was lacking in quality with mainly half scoring chances the order of the day.
Sam Allardyce would be happy with the improvement made by the Hammers following their last away loss to Swansea City (3-0) whilst Chris Hughton will be hoping for better from his side who have now recorded three draws in a row.
Norwich had two penalty claims in the first half with an early one coming when Robert Snodgrass went down near the byline but Kevin Nolan had pulled out of the challenge with referee Chris Foy making the correct call.
Late in the opening term, Norwich almost won a penalty when Andrew Surman went down on the edge of the box under a challenge from James Collins but Foy rightly awarded a free-kick instead which the Canaries made nothing of.
Both sides had half chances throughout the first half with Hammers keeper Jussi Jaaskelainen called on to make a few saves in quick succession when the Canaries pressed the visitors' goal.
Substitute Kane almost curled one in late in his Norwich debut before having an even better chance when played in by Snodgrass but was unable to beat Jaaskelainen one-on-one.
Snodgrass then had a great opportunity to win it for the home side when Kane found him from the left but Joe O'Brien was able to clear off the line to allow his side a share of the points which takes them to seven from five outings whilst Norwich find themselves sitting 13th win three draws and a loss from their four fixtures under Hughton.
Carrow Road, Norwich - 26,806
Yellow cards:NOR - nil WHU - James Collins 40'