Huckerby proved a constant menace to Albion but Norwich were unable to make the most of his trickery as their finishing let them down.
They dominated in terms of chances created and Albion were fortunate that they were able to escape with their unbeaten home record still intact.
Albion simply had no answer to the skills of Huckerby who had rejected a move to The Hawthorns last season in favour of joining Norwich from Manchester City.
Albion did not hit the heights they had reached in their previous game against Bolton when they recorded their first victory of the season.
That was perfectly summed up the fact that Albion's goalscorers against Bolton, Kanu and Zoltan Gera, were both taken off in the second half.
But by then Norwich should have been well on the way to collecting their first three points of the season as they could have been comfortably in control by half-time with Albion simply having no answer to the trickery of Huckerby.
He began terrorising them as early as the ninth minute.
After Gera had given Norwich an early scare with a 20-yard drive that flew inches wide, Huckerby took control.
He picked out Leon McKenzie with a right-wing cross that caught the Albion back four napping.
But McKenzie was unable to get his shot from six yards on target when he only had goalkeeper Russell Hoult to beat from six yards.
Huckerby then tested Hoult with a stinging drive in the 24th minute after a mazy run into the Albion area before wasting the best chance of the half 60 seconds later.
McKenzie dispossessed the Albion central defender Darren Moore before releasing Huckerby only for the former Manchester City forward to slice his shot horribly wide from 12 yards after he came under pressure from full-back Bernt Haas.
Norwich were let down by their finishing again 12 minutes before half-time when Mattias Jonson fired into the sidenetting from close range after another neat pass by Huckerby.
Albion struggled to make much of an impression themselves in attack and ironically their best chance to score in the first half came courtesy of the Norwich midfielder, Gary Holt.
He deflected a cross from Haas towards his own goal and it needed a superb one-handed save from Robert Green to keep Norwich on level terms.
While a half-time roasting by manager Gary Megson did fire some life into Albion, it was Norwich who still looked the most threatening side.
But Jonson wasted another clear chance after 52 minutes when his point-blank header from a David Bentley cross was palmed away at the near post by Hoult.
Albion's threat was more sporadic but when they did create an opening they found Green to be in inspired form.
Albion substitute Robert Earnshaw set up Jonathan Greening in the 61st minute and the former Middlesbrough midfielder whipped in a fierce drive from 20 yards.
Green managed to block that shot and was then alert enough to flick the loose ball away from striker Geoff Horsfield.
Man of the Match: Darren Huckerby – The Canaries forward terrorised the Baggies defence without being able to fashion a priceless winner for his side.