Tommy Rowe’s 22nd-minute sweet opener put Rovers on course for maximum points after a bright start at the DW Stadium.
But Yorkshire official Nield awarded a free-kick to the hosts just two minutes later which they equalised from through Will Keane’s header.
And it was Keane who compounded the visitors’ misery when he bagged a second goal of the afternoon, stabbing home from close-range seven minutes after the restart.
“I’m here fighting for my life and you get officials that cannot see the most blatant offside you will ever see,” blasted Wellens.
“I feel like I’ve run over another black cat, but I’ll pick my players up. We arrived with a game-plan, but it’s not the game-plan we want to do long-term.
“We tried to frustrate them, did that to a tee and we go 1-0 up, but then the referee gives a pathetic free-kick away which they scored from.
“I’ll get fined for going over the top but they (the officials) won’t get fined for their performance. I’m proud of my players because I thought they were very good.”
Rowe’s opener was Rovers’ first goal in eight games in what has been a dismal start to the season which now shows five defeats from their opening six league fixtures.
But Keane levelled almost immediately and snatched winner to inflict further misery on Wellen’s misfiring side.
Wigan Athletic: Amos, Power, Whatmough, Watts, Darikwa, Naylor, Cousins, Lang (Edwards 79), Keane, McClean (Jones 79), Wyke (Humphrys 86). Unused substitutes: Pearce, Tilt, Bayliss, Tickle.
Doncaster Rovers: Dahlberg, Knoyle, Williams, Olowu, Rowe, Close, Galbraith (Gardner 70), Seaman (Vilca 57), Dodoo, Smith (Bostock 80), Hiwula-Mayifuila. Unused substitutes: Jones, Greaves, Horton, Ravenhill.
Referee: Tom Nield (Yorkshire)