The Magpies already knew they were promoted courtesy of Nottingham Forest's 0-0 draw with Cardiff when they ran out at St James' Park, but the mood took a turn for the worse when Richard Cresswell's header, which Darius Henderson may have got a touch to on the line, put the visitors into a 22nd-minute lead.
However, Peter Lovenkrands levelled from the penalty spot on the stroke of half-time and Nolan's 73rd-minute scissor-kick finish was enough to secure another three points and take his side six points clear of second-placed West Brom, who have played a game more.
Hughton congratulated his players and staff on the pitch as they warmed up, but then the focus turned swiftly to the business of securing the Championship title.
However, they were made to work throughout by a Blades side who arrived on Tyneside with their play-off hopes still alive.
Wayne Routledge should have done better when he was played in by Nolan early on, but he could not hit the target, although Cresswell was guilty of a similar miss at the other end with 17 minutes gone.
But the striker made amends five minutes later when he met Harper's corner with a glancing header, which Henderson appeared to get a touch to right on the line, as the Magpies conceded just their 10th league goal at St James' Park this season.
Routledge, Andy Carroll and Lovenkrands all went close in a flurry of activity as the half-time whistle approached, but Newcastle got themselves back on terms in the final minute of the half.
Referee Andy Hall awarded a generous penalty for Chris Morgan's untidy challenge on Carroll as Guthrie's corner came in, and Lovenkrands sent goalkeeper Steve Simonsen the wrong way from the spot to level with his 15th goal of the season.
Just as they had done in the first half, the Blades started strongly after the break with the home side misfiring until Lovenkrands smashed a stinging shot just over on the hour.
The Dane really should have given the Magpies the lead three minutes later after being played in by full-back Jose Enrique, but he fired wide with just Simonsen to beat.
Gutierrez went agonisingly close with 20 minutes to play when he sped past Nyron Nosworthy and cut inside, only to see his shot come back off the foot of the post with Simonsen beaten.
But the breakthrough finally came two minutes later when Lovenkrands headed down Danny Simpson's ball to Nolan, who acrobatically blasted it home to also take his tally to 15.
Guthrie might have made certain of the points with 80 minutes gone, but was denied by Simonsen, although the party among a crowd of 48,270 was already well underway.