The Blades took the lead with 17 minutes left to play after a controversial penalty was awarded by referee Andy Madley, following a lengthy consultation with VAR.
Sheffield United dominated large parts of the game, but much like we've seen this season, their biggest struggles came in the final third.
The three points takes Chris Wilder's men nine points off 17th place Brighton.
Story of the match
The former Republic of Ireland international had his first chance came after a lovely move from Blades trio Oliver Burke, Ethan Ampadu, and John Lundstram before the latter slid McGoldrick in, but he was unable to orchestrate enough bend on his shot to beat Karl Darlow in the Newcastle goal.
There were plenty more half-chances for Wilder's men, with Lundstram firing just wide, before a late flurry of chances came from Jayden Bogle and Oliver Burke.
McGoldrick's best chance of the half came as Ampadu picked him out with a perfectly weighted cross to the back post. However, the former Ipswich man was unable to force Darlow into action, as his header sailed over the bar.
Newcastle's game plan looked clear from the off. Steve Bruce had set up his side to absorb the pressure, as the Magpies looked to punish them on the break, from their pacey frontline which consisted of Ryan Fraiser, Callum Wilson, and Jeff Hendrick.
Newcastle had a penalty appeal turned down by VAR just before halftime. Bruce's side questioned whether John Eagan's clearance seemed to brush his own hand. But after various replays at different angles and speeds, the answer was no from the VAR assistants at Stockley Park.
Any hopes Newcastle had of catapulting themselves up the table with three points tonight , were dealt a huge moments before the interval when Fraiser was shown two yellow cards in as many minuets, following two late challenges on Fleck and McGoldrick.
Wilder's intent to punish 10 man Newcastle was made clear very early into the second half. As both Rhian Brewster and Billy Sharp were introduced, as the Blades looked to reshuffle their pack in the hope of finding that elusive first win of the season.
Even with the 9 black and white shirts outfield, Newcastle still posed a dangerous threat to Aaron Ramsdale's goal, even if Wilson was forced to feed off scraps for the majority of the second half.
It wasn't long before VAR controversy stuck again, late in the second half. As Sharp battled it out in the penalty area Federico Fernandez was deemed to have knocked the ball out of the strikers path with the use of his hand. Madley's stay at the VAR screen was short and sweet and his swiftly awarded a penalty to the home side.
Sharp placed the ball down twelve yards from goal before cleanly dispatching the ball into the bottom left corner, sending Darlow the opposite way in the process. The sound of the net rippling was met with thunderous roar from the United bench.
It was always going to be a restless finish at Bramall Lane and there was time for one last heart-in-mouth moment. In the 96th minute Bogle failed to deal with one of Newcastle's late launches, as his back pass nearly trickled past the onrushing Ramsdale and into his own net, luckily for the United defender it crept just wide of the post.
Sheffield United XI: Ramsdale, Basham, Egan, Ampadu, Bogle, Lundstram, Norwood, Fleck, Osborn, McGoldrick, Burke
Newcastle United XI: Darlow, Yedlin, Clark, Fernandez, Schar, Dummett, Hendrick, Hayden, Sean Longstaff, Fraser, Wilson