Manager Rafa Benitez was furious, apparently believing a covering defender was in position to prevent an attempt on goal.
He also felt Newcastle should have had a penalty when their goalscorer Ayoze Perez was elbowed near the end.
Promoted Wolves, who had beaten Chelsea 2-1 on Wednesday after six games without a win, went ahead in the 17th minute with Diogo Jota's second goal of the week.
Newcastle equalised six minutes later when Salomon Rondon, having crashed a free kick against the bar, crossed for Perez to score.
But Doherty's last-gasp header after Newcastle keeper Martin Dubravka had saved Jota's shot pushed Wolves into the top half of the table and left Benitez's side 15th, three points above the bottom three.
"Scoring with almost the last kick of the game gives them no chance to get back into the game, so it's pretty special that way," Doherty said.
Wolves had two of their numerous Portuguese players to thank for the opening goal. Helder Costa spotted that Jota was unmarked and found him with a perfect cross to chest the ball down and score.
They had started well but soon came under pressure and conceded an equaliser.
Rondon deserved a goal with the fierce free kick that came back off the bar but he chased the ball down and crossed for Perez to glance in a clever header.
Newcastle were forced into a change at halftime with Spanish defender Javier Manquillo coming into the back three for the injured Federico Fernandez.
They suffered a huge blow with Yedlin's red card, for a blatant pull on Jota's shirt after he had gifted possession to the Wolves man, and were fortunate when substitute Raul Jimenez hit the underside of the bar.
Dubravka seemed to have preserved a point with a fine save from Doherty 10 minutes from time but right at the end he could only parry Jota's shot and Doherty had an open goal to head into for his team's second win in five days.
Perez, however, was adamant that he had been elbowed in the face by Willy Boly a few minutes earlier.
"The guy elbowed me really hard straight in my nose but the referee said it was the ball that hit me, even though I was bleeding," he said.
"I don't know what we need to get a penalty."
It was Wanderers' first win in the top flight at Newcastle since 1959, when they last won the title.
(Reporting by Steve Tongue; editing by Martyn Herman)
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