The 31-year-old was left without a club in the summer after his contract at Ipswich Town was not renewed, but impressed the Blades enough on trial to earn a deal at Bramall Lane.
His winner against Queens Park Rangers on Saturday was his 10th goal of the season – and his fifth in the last six games – to help United leapfrog second-placed Norwich City into the Championship’s automatic promotion places.
Alongside captain Billy Sharp, the pair have banked 27 goals between them and Blades manager Wilder believes Nottingham-born McGoldrick has flourished since swapping Portman Road for Bramall Lane.
“He has been an important player for us,” said Wilder after the Blades picked up their fourth successive Championship win.
“Sometimes you need that change of environment, change of scenery, something fresh.
“He definitely suits the way we play, and I would imagine if you ask him he is really enjoying his football. It’s a good club, treat him well, and the players are a good group to work with.
“We allow him to go and express himself and he has been outstanding, as a lot of players have.
“He has had a really good Championship career and he is continuing that. He is a great lad, a down-to-earth funny guy who works hard.”
In a game of few genuine chances, the best two opportunities to break the deadlock against Rangers fell to McGoldrick. United opened up the Rangers defence as early as the fourth minute.
A beautiful diagonal ball from George Baldock picked out the run of Sharp down the left flank, but with the angle a little narrow to beat Joe Lumley, Blades’ captain unselfishly tucked the ball inside for strike partner McGoldrick.
The chance maybe caught the Republic of Ireland international off guard, as he dragged his shot wide of the post from the penalty spot.
The former Sheffield Wednesday loanee, though, was more ruthless with his finishing on 37 minutes with what proved to be the only goal of the afternoon.
The striker had earlier kept the ball in play, rather than accept a Blades throw-in, before switching play to the right flank.
United kept possession before Ollie Norwood’s cross was headed in at the near post by McGoldrick.
Rangers – who came into the match on a six-game unbeaten run – rarely troubled United’s goal.
In fact their only first-half attack worthy of note came when Ebere Eze left fly from 40 yards. But even a deflection failed to cause Blades goalkeeper Dean Henderson any trouble in collecting the ball.
It did not get any busier for Henderson in the second half, with defences on top at both ends of the pitch.
Luke Freeman fired tamely at the goalkeeper before then firing wide.
Wilder sent on Kieran Dowell – the on-loan midfielder from Everton – and Leon Clarke to try to find that elusive second goal.
A couple of headers from Chris Basham and John Egan failed to trouble Lumley, and Enda Stevens shot wide from a promising position.
“It was a good, solid performance,” said Wilder. “It wasn’t spectacular, there’s a lot of plaudits for our work with the ball, but I also thought we did well without it, we looked really solid.
“We have to compete first and play second.
“We’ve done that in difficult conditions at times and, along the way, we’ll have these games where we have to be nice and composed and patient to get the right result.”
Victory cut Leeds United’s lead at the top of the Championship to four points, with 19 games of the season left. While this win lacked the style or panache of festive victories against Derby County, Blackburn Rovers and Wigan Athletic, the Blades just did enough to take all three points off Steve McClaren’s team.
This was mainly due to a watertight defence – recording their third Championship clean sheet in a row – with Chris Basham, Jack O’Connell and Egan commanding at the back.
The Blades have two testing trips to Swansea City and Norwich on the horizon this month, but Wilder’s team look like they can last the distance this season.
“There’s a really good saying about ‘heavy shirts’ and I don’t think we have had heavy shirts in my time here,” said Wilder.
“There have been teams – and players – that have played here that have had that weight, the expectation, and we try to lift that off them, as a staff, to give them the freedom to go and play.”
Sheffield United: Henderson, Basham, Egan, O’Connell, Baldock, Norwood, Fleck, Stevens, Duffy (Dowell 68), McGoldrick (Stearman 90), Sharp (Clarke 84). Unused substitutes: Moore, Madine, Johnson, Coutts.
Queens Park Rangers: Lumley, Furlong, Leistner, Lynch, Bidwell, Wszolek (Osayi-Samuel 62), Cousins (Smith 73), Scowen (Chair 84), Freeman, Eze, Wells. Unused substitutes: Ingram, Hall, Manning, Oteh.
Referee: A Woolmer (Northants).