In yet another game littered with controversial refereeing decisions, Shaun Maloney curled home in magnificent style from a corner that should never have been.
That came after a disallowed goal for Victor Moses in the first half, with a clear handball against Maynor Figueroa thrown in for good measure.
The result was the first time Wigan had ever avoided defeat in 15 meetings with their north-west neighbours, and condemned United to their first reverse since January.
After the debacle of Stamford Bridge, where they conceded two goals that were clearly offside and a red-card punch by Branislav Ivanovic on Maloney, Wigan must have thought they had endured as much misery as possible at the hands of officials.
But the mystifying events on the half hour merely provided more ire in the Latics camp.
When Dowd initially signalled a goal as Moses powered home his header, no United players headed towards the referee to complain. However, assistant Dave Richardson, spotted something the referee had missed, namely Gary Caldwell blocking David de Gea on the line.
Stood on the touchline, Martinez was incredulous. And when he was informed by the fourth official why the goal had not been given, the Spaniard was even more furious.
The goal would have been the least Wigan deserved for an outstanding first-half performance, in which they denied United the time and space to display their obvious talents.
Sir Alex Ferguson's presence on the touchline for long periods was evidence all was not well in the United camp.
James McCarthy had a shot tipped over by De Gea before the disallowed goal and Wigan wasted a number of free-kick opportunities, most of which were earned by Franco di Santo's industry.
However, the recurring inability to find the net - in legal fashion - which has undermined Wigan's stylish approach all season was causing concern.
A Ryan Giggs flick that almost released Javier Hernandez and a blocked Wayne Rooney shot in the final minutes of the half were obvious reasons for the hosts to worry.
When questioned a couple of weeks ago about whether big clubs are favoured by referees - after Fulham's Danny Murphy was denied a last-minute penalty at Old Trafford - Ferguson stuck his colours firmly to the mast of such decisions evening themselves out.
And the evidence came four minutes after the restart.
As soon as Dowd awarded a corner following Phil Jones' tangle with Jean Beausejour, the United man indicated the referee had got it wrong.
Those pesky TV cameras proved it too. Jones never got near to the ball as it rolled out of play.
No-one from the Wigan camp was apologising, though, as Maloney exchanged passes with Beausejour, skipped round Rooney and curled a delightful shot past De Gea.
Having already introduced Tom Cleverley at half-time, Ferguson took decisive action, first by bringing on Danny Welbeck, then introducing Nani - back after five weeks out with an ankle injury - with Rooney the man replaced, without a hint of protest.
Then came the second vital call on Wigan's behalf as Maynor Figueroa clearly blocked Jones' cross with his arm, but there was no penalty.
United attempted to shrug off the disappointment by forcing their way through the Wigan defences but there was no way through, with Nani and Michael Carrick wasting the best chances to spoil a famous night for the Latics, whose full significance will only become known in five games' time.