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 taste a league victory for the first time since July.
Newcastle, reduced to 10 men when Ryan Fraser was sent off just before half-time, 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.
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.
The hosts' manager Wilder summed up his feelings after the whistle.
"[186 days without a win...], I have been counting! Every minute of every hour of every day! It feels good, I'm delighted," said Wilder, who got the Sheffield club promoted back to the top flight in 2019.
"We should have got more results, we know that, but the performance was good. We played with the identity that has been the way we have played for the last few years.
"I imagine the sending off and the penalty will be talked about, but in my opinion we were value for the victory tonight."
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.