The win should have been more emphatic but Brian Jensen pulled off some important second-half saves to deny Paul McVeigh and substitute Leon McKenzie.
Youssef Safri was unlucky to be credited with Burnley's consolation goal when Jon Harley's long-range shot took a massive deflection off the Moroccan's boot.
The home side kicked off attacking the Barclay End goal but although most of the play was in the other half, it was the 16th minute before Norwich went ahead.
The lively Safri played a free-kick to Charlton in the inside left channel and his left-foot angled drive beat Jensen from eight yards.
Six minutes later Huckerby's snap-shot almost made it 2-0.
Burnley came more into the game and former Canary Ade Akinbiyi put a couple of headers wide of the target.
A rare Huckerby header gave Dean Ashton a shooting chance but he opted for power and blasted the ball high and wide.
However, when Ashton picked out Huckerby with a precise cross-field pass, he finished the move with a right-foot shot from 17 yards that curled inside Jensen's left-hand post.
After 50 minutes Huckerby fired inches over the bar, while at the other end Gifton Noel-Williams did well to fashion a shooting chance but only succeeded in chipping the ball over the bar.
McVeigh chipped Jensen but the ball was headed off the line by Jon Harley and the clearance was completed by John McGreal.
Ashton limped off to be replaced by McKenzie with 25 minutes to play.
Burnley scored their goal when Harley's shot deflected off Safri and looped over Robert Green on 73 minutes.