Against a Walsall side scrambling for points at the wrong end of the table but which, on this evidence at least, looks in no danger of the drop, United slipped to their first defeat since August and passed up the opportunity to regain second place.
Amadou Bakayoko scored the only goal of a bad-tempered contest which also saw Billy Sharp miss a late penalty.
But Wilder’s frustration at referee Darren England’s performance - he disallowed another effort from United’s captain in added time - was nothing compared to his disappointment at their’ failure to fathom a way past Walsall’s defence.
For long periods United, who remain third in the table behind leaders Scunthorpe and Bolton, were erratic as their passing went astray. Nevertheless, despite Walsall demonstrating an in-depth knowledge of the dark arts as the evening wore on, they should have secured at least a draw.
Paul Lambert’s decision to attend this game provided another fascinating sub-plot to a contest which, not for the first time in recent weeks, saw United fail to translate possession into goals.
The Wolverhampton manager, who has yet to reveal if Ethan Ebanks-Landell will remain in Yorkshire beyond January, insisted he must personally run the rule over his qualities before a final decision is made.
Knowing that every kick, every tackle and every header he made could decide where he spends the next phase of his career meant the 23-year-old entered this match under intense pressure. It left United in a quandary too.
Wilder is loath to lose a player whose presence has helped transform his team into serious promotion contenders. United concede less than a goal per game and keep more than double the number of clean sheets with Ebanks-Landell in their rearguard. Wilder will not have wanted Ebanks-Landell to produce a below-par display. But, having watched him struggle against Erhun Oztumer, knows United’s chances of keeping him until the end of the season might just have increased.
Lambert was not the only recognisable face sat in the stands, with Bolton manager Phil Parkinson and his assistant Steve Parkin also running the rule over Wilder’s charges ahead of Sunday’s FA Cup tie at the Macron Stadium. Kevin Davies, the former Wanderers centre-forward and lifelong United supporter, was also in attendance, albeit as part of an initiative designed to attract more youngsters to watch EFL clubs.
United’s chequered performance, at least until Duffy seized the fixture by the scruff of the neck midway through the first-half, will have done little to help his cause.
Oztumer, who was born in Greenwich but learnt his trade on the banks of the Bosphorus, rattled the woodwork with a cheaply conceded free-kick before Bakayoko prodded home his seventh goal of the season.
Strangely, the centre-forward pounced just as United were threatening to seize control. But Walsall had already served warning they would pose a threat.
Jake Wright’s contribution has gone largely unnoticed in recent weeks as the likes of Ebanks-Landell and Fleck have grabbed the limelight. But his ability to impose himself on situations undoubtedly contributed to United’s downfall.
Oztumer’s long ball over the top should have been comfortably dealt with by United’s defence. Instead, a lack of decisiveness allowed Bakayoko to dart through and claim perhaps the simplest goal he will score this term.
Whitney’s makeshift 3-5-2 formation raised eyebrows before kick-off.
But the surprise provoked by his selections paled into insignificance compared to the shock United’s woefully slow start caused.
Walsall, overhauling their tactics to match-up against opponents missing the injured Wright, chased, harrassed and harried the hosts into a series of uncharacteristic errors during the early exchanges. Indeed, only the width of the crossbar prevented Oztumer from giving them a 10th minute lead.
Leon Clarke glanced a header wide at the other end of the pitch. But, until Duffy put Walsall briefly on the back foot, United appeared strangely subdued.
When Jack O’Connell saw a 36th minute header scrambled off the line following Paul Coutts’ corner and Daniel Lafferty forcing Neil Etheridge to save at the foot of his near post, the momentum looked set the shift.
Bakayoko, though, ensured it turned back in Walsall’s favour by sliding home past the advancing Simon Moore three minutes before the interval. When Oztumer came within a whisker of doubling Walsall’s lead at the beginning of the second period, it became clear United were facing a real test.
Sharp saw a strong penalty appeal waved away by referee Darren England just past the hour mark as the pressure on Walsall cranked-up a notch before James O’Connor handled John Fleck shot.
Sharp stepped-up to take the penalty but saw his 84th minute attempt gathered by Neil Etheridge.
He did beat Walsall’s goalkeeper soon after but adjudged to have turned the ball home with his hand.
United: Moore, Fleck, O’Connell, Basham (Chapman 69), Sharp, Coutts, Freeman, Ebanks-Landell, Duffy, Lafferty (Lavery 80), Clarke. Not used: Hussey, Scougall, Done, Ramsdale, Brown.
Walsall: Etheridge, Edwards, Laird, O’Connor, McCarthy, Dobson (Osbourne 69), Chambers, Oztumer (Ginnelly 69), Morris, Preston, Bakayoko (Jackson 77). Not used: Cuvelier, MacGillivray, Kinsella, Makris.
Referee: Darren England (South Yorks).