Clear chances were scarce at a rain-soaked Bramall Lane, United's home ground
But McGoldrick had a brilliant opportunity after just 14 minutes when the Blades were awarded a penalty for a foul on Mark Duffy by Morgan Fox inside the box.
A tame effort, however, was saved by Wednesday goalkeeper Cameron Dawson.
With Wednesday defending in depth as they ended a run of four straight defeats, United couldn't find a way through and had to settle for a point in the 'Steel City' derby -- the northern English city of Sheffield has long been regarded as the home of Britain's steel industry.
But the draw was still good enough to see United go level on points with Championship leaders and Yorkshire rivals Leeds United, who remained top on goal difference ahead of the bulk of this weekend's fixtures.
"It was a massive moment that penalty save and absolutely huge to do it in front of our own supporters," Dawson told Sky Sports."We dug in there and fought right until the end."
Sheffield United striker Billy Sharp, who went close with a header late on, added: "We got the penalty, a great chance, but after that, we just couldn't break them down.
"I should've put that header away at the end. I thought I got enough on it, but then I saw it just sail past the post."
Only the top two sides at the end of the regular season are guaranteed promotion to the lucrative Premier League, with the other spot going to the eventual winners of a series of post-season play-off matches involving the teams finishing in third to sixth positions.