Chris Wilder’s side had failed to win any of their opening 17 matches of the season – the worst start to a Premier League campaign – but finally came good to leave the pitch with three points in the bag for the first time in six months.
Newcastle, reduced to 10 men when Ryan Fraser was sent off just before halftime, were abject and could have few complaints as their winless league run extended to six matches.
Sheffield United dominated the first half with Dave McGoldrick twice going close and they were eventually rewarded in the 73rd minute when substitute Sharp coolly converted from the spot after Federico Fernandez was adjudged to have knocked the ball away with his hand under pressure from Sharp.
Rhian Brewster’s deflected shot nearly made it 2-0 but the ball rebounded off the post and the hosts endured a nervy finale with Jayden Bogle going dangerously close to an own goal.
There was huge relief when the final whistle sounded seconds later and while Wilder still faces a monumental task to try to keep the club up, the mood of gloom hanging over Bramall Lane has been lifted, at least temporarily.
Victory more than doubled Sheffield United’s points tally to five although they remain rock bottom and nine points behind Brighton and Hove Albion who sit one place above the drop zone.
“It’s a huge relief, I’m so happy for the boys. It was important we got a win soon. It was scrappy at times but in the first half I thought we were brilliant,” Sharp said.
“Everyone has written us off, the pressure is off. We’ve not had a great time in the last few months but we’ve got to keep our heads high now. We’re good enough to do it.”
Sheffield United looked anything but a team without a league win in their last 20 matches, including at the back end of last season, as they attacked in waves in the first half.
McGoldrick forced a smart save from Karl Darlow after a neat build-up and then headed wide from Ethan Ampadu’s cross.
Darlow also did well to save from Bogle before Fraser picked up two bookings in quick succession just before the interval, the second for clipping McGoldrick.
It was attack versus defence after the break but Newcastle held firm until a long ball forward saw Sharp and Fernandez in a race.
Fernandez appeared to nudge the ball with his hand and when referee Andy Madley was invited by VAR to review the incident on a touchline monitor he pointed to the spot.
Sharp took a few deep breaths and sent the excellent Darlow the wrong way.
There was nearly late heartbreak though when Bogle attempted to chest a ball back to his keeper Aaron Ramsdale and watched in horror as it almost ended in the net.