The 35-year-old, out of contract at the end of the season, struck the winner in the 59th minute to keep the Canaries - boosted by the part-opening of the new South Stand which allowed an extra 3,000 supporters into Carrow Road for the crunch clash - two points clear of second-placed West Brom.
It was also the 94th goal of Roberts' Norwich career - and one which could go a long to way towards securing their Premiership dream.
The goal came seconds after United had a penalty appeal waved away by referee Barry Knight after he failed to spot a tug by Norwich defender Craig Fleming on Michael Tonge.
Norwich broke and Huckerby went on a run down the left wing. His cross was only partially cleared and veteran Roberts slotted home.
Wayne Allison then fired over for the visitors before team-mate Paddy Kenny pulled off a fine save to deny Roberts a second.
The Blades brought on former Norwich forward Paul Peschisolido with 17 minutes left as they tried to get back on level terms.
But it was Paul McVeigh who so nearly put the result beyond doubt, only for Kenny to save United again.
Kenny, whose last-minute howler gifted Derby a second goal in the defeat at Pride Park on Wednesday, came to his side's rescue again to keep out a towering header by Malky Mackay.
United manager Neil Warnock's trump card nearly paid off with 13 minutes remaining when Peschisolido almost grabbed the equaliser only for Norwich goalkeeper Rob Green to foil him.
Chances continued to be created by both sides and Roberts sidefooted a shot wide while Allison missed a great chance to restore parity.
Wales international defender Robert Page and Allison earlier wasted good chances to give United a half-time lead.
Tonge delivered a fine cross which Page met but he somehow headed wide with the goal gaping in the 32nd minute - then Allison headed over Alan Wright's cross moments later.
For Norwich, Huckerby flashed a shot wide while the blustery conditions nearly caught out Kenny as Damien Francis' shot caught the elements and came close to sailing into the net.
But Norwich held on to claim their first win in 2004 - and one which edges them closer to a return to the top-flight.