The pacy striker put the visitors ahead shortly before half-time when he nodded home Youssef Safri's corner.
Huckerby then turned provider when he supplied the cross for Dickson Etuhu to head in after the break.
Andy Dawson smashed in a 30-yard free-kick late in the game after Etuhu fouled Samuel Ricketts, but it proved too little too late for Hull.
Hull boss Phil Brown:
"Credit to Norwich - they did a turn on us. But we'll keep on fighting as the lads at Hull City have got tremendous character.
"Now we have five games remaining to get ourselves right out of it."
Norwich boss Peter Grant:
"There are a lot of very good players in this division and Darren is up there with the best of them.
"He's got that little bit of quality, he's a match-winner and you'll go far to find someone who can excite and frustrate you in the same moment.
"I questioned him a few weeks ago after the Wolves game a few weeks ago when he was magic, but his final ball was poor. Now he's answered me superbly."
Hull: Myhill, Ricketts, Turner, Delaney, Dawson, Parlour, Ashbee, Peltier (Marney 70), Forster (Vaz Te 60), Windass, Elliott (Barmby 52).
Subs Not Used: Duke, Coles.
Booked: Myhill.
Goals: Dawson 88.
Norwich: Warner, Lappin, Shackell, Doherty, Drury, Croft (Fotheringham 71), Safri, Hughes, Huckerby (Martin 90), Etuhu, Dublin.
Subs Not Used: Gallacher, Renton, Eagle.
Booked: Hughes, Warner.
Goals: Huckerby 39, Etuhu 55.
Att: 19,053
Ref: M Thorpe (Suffolk).