The mistake was Simon Grayson's; its cost, a reduced group of six substitutes with not a single striker among them. To complicate his job further, two players chosen to start at MK Dons were injured inside 63 minutes, reacquainting Grayson with the lack of control caused by stretched resources.
That has been the domain of other managers in United's division this season. Against that backdrop, the final straw could have been the laboured tone of his players' collective performance, but there are few situations in which Leeds seem unable to find a crumb of inspiration.
Disrupted, weakened and slightly out of sorts, the priceless winning goal scored by Robert Snodgrass three minutes into injury-time implied that their season can only end one way.
Inspiration In forcing that goal - the only one scored on an afternoon when inspiration was every bit as scarce - Leeds were gratefully assisted by a straight red card shown to Jason Puncheon, a hindrance which to Paul Ince's mind outweighed every factor constraining Grayson.
Puncheon's dismissal at the very end of the first half convinced MK Dons that the victory they had been unable to set up before the interval would likely prove unattainable with only 10 players, but even the goalless draw his team were 60 seconds from completing might have struck Ince as an opportunity missed.
If not exactly vulnerable on Saturday, United's dwindling head-count and lacklustre persona made them as susceptible to defeat as they have been this season, the first time a victory has relied on sheer will.
Four days after the club's Carling Cup tie against Liverpool, Grayson did not anticipate a steep descent in Milton Keynes from the commendable standard his players reached at Elland Road on Tuesday night, but the drain on their imagination was perhaps more extreme than he had expected.
Before half-time, Leeds failed to concoct a shot on target. That father-to-be Becchio was not involved did not appear entirely coincidental.
The Argentinian was expecting his first child over the weekend and he remained in Yorkshire when United's squad left for Milton Keynes on Friday after his wife went into labour.
Becchio's qualities are a subject of almost weekly appreciation but the striker's style is such that his strengths are almost more conspicuous by their absence.
Without him, Jermaine Beckford was quickly isolated and United's midfield grew detached from Beckford and Mike Grella until a rush of blood from Puncheon in first-half injury-time gave the visiting players more freedom to roam.
Puncheon's crime was a two-footed tackle on Michael Doyle on the halfway line, a challenge that swiped the ball with one leg and Doyle with the other.
Grayson was charitable, defending Puncheon as "not that type of player", though it did not stop him from remonstrating with the midfielder as he walked towards the tunnel.
Ince said the tackle was "probably in between a yellow and a red", as close as he was going to come to concurring with referee Andy D'Urso, who was not intent on making friends in Milton Keynes, try though he did to influence proceedings.
D'Urso had earlier refused to bend when Leeds realised before kick-off that Showunmi's name was unintentionally missing from their teamsheet, a careless error which Grayson held his hands up to.
Showunmi warmed up with the rest of United's players, intending to take a place on the bench, but D'Urso was unwilling to allow an addition to the original squad which had been submitted to him.
Leeds, as Grayson later conceded, were in no position to argue. The contentious involvement of the Essex official - a man dropped from the Select Group list in 2005 - did not end there but a fussy performance in a match dominated by his whistle did more damage to MK Dons than it did to Leeds.
In mitigation, the constant sniping which numerous players were guilty of, hardly helped.
Puncheon's foul was reckless enough to warrant the red card D'Urso showed to him. Ince's complaint was rather one of consistency, aimed towards the referee and indirectly at Snodgrass.
Twenty minutes before the dismissal of Puncheon, Snodgrass incurred punishment by reacting to a clumsy tackle from Dean Lewington by pushing the defender in the back of the head.
D'Urso had the option of applying the letter of the law and red-carding Snodgrass, soft though the dismissal would have been. Instead, he limited himself to a caution.
The consequence of that leniency was the late header with which Snodgrass settled an important game. Before his winning goal, it had taken Leeds fully 45 minutes to settle into the match.
Patrick Kisnorbo and Jermaine Beckford guided efforts over the crossbar in quick succession at the end of the first half but they were tepid replies to the few chances and general control enjoyed by MK Dons.
Saturday's game was a meeting between League One's leaders and the division's fourth-placed club, but reasonable predictions of an open and eager fixture were unfounded.
A sense of muddled dislocation hung over both teams and Ince's sensible response to Puncheon's dismissal - constructing a five-man midfield and leaving the cumbersome Aaron Wilbraham as a lone striker - added to the congestion.
In the first half, ilbraham's scuffed shot allowed Shane Higgs to gather easily after Leigh Bromby's sliding tackle robbed Jemal Johnson of possession and diverted it to the feet of Ince's tall forward 10 yards from goal, and Higgs was on hand again with a low parry when Puncheon attacked his goal from long range a minute before his dismissal.
Leeds did not draw an especially flattering comparison with Ince's side before half-time, though the loss of Jason Crowe to a pulled hamstring after seven minutes did nothing to help.
With an hour gone, Grayson found himself making another enforced and unwanted change when Higgs injured a thigh.
It seemed to be one of those days. As United's advantage of numbers took effect, Howson picked out Beckford's angled run into the box and saw the striker clip the ball into Willy Gueret's net at the very moment that an offside flag rose on the sideline.
Howson himself found Gueret badly exposed with five minutes to play but drilled a low shot against the foot of Darren Powell, stationed on the goalline.
Grayson had no additional cards to play by that stage but his players produced one last trick as the game crept into a third minute of added time.
Bradley Johnson was bundled over on the left wing but composed himself to pick out Snodgrass in a crowd of players with a free-kick which the Scot nodded through Gueret's hands.
Snodgrass sprinted straight to the away dug-out, acknowledging a coach whose midas touch grows stronger by the week.
On the club's last visit to MK Dons, United's players effectively sacked their manager. Grayson need have no such fears.