David Connolly's 86th-minute penalty gave Wigan a deserved win and put them into the Carling Cup quarter-finals.
Wigan laid siege to the Newcastle goal but missed a host of chances before finally breaking the deadlock.
Referee Steve Bennett pointed to the spot as Robbie Elliott challenged Jason Roberts, and Connolly scored with ease.
Emre hit a post and Scott Parker came close, but Newcastle were fortunate to survive for so long as under-strength the Latics turned on the style.
Wigan now go into Saturday's last eight draw as their dream season continues.
Boss Paul Jewell made nine changes to his side, but Newcastle counterpart Graeme Souness paraded a strong team, including Alan Shearer but without the injured Michael Owen.
Jewell's men may have been weakened, but they should have been out of sight after a vibrant first-half showing.
Connolly's cross flew across the face of the area to Lee McCulloch, whose effort went narrowly wide.
Ryan Taylor's free-kick then tested Newcastle goalkeeper Shay Given, who saved at the second attempt.
Newcastle's goal was leading a charmed life, and twice Andreas Johansson should have given them the lead, first with a looping header that was saved by Given and then when he turned a weak finish into the keeper's arms from only eight yards after good work by Taylor.
Wigan suffered a blow after 29 minutes when Emerson Thome appeared to suffer a serious cheekbone injury in an accidental collision with Parker and was replaced by Stephane Henchoz.
McCulloch went even closer for Wigan before Nolberto Solano cleared Matt Jackson's header off the line.
Given then made a superb double save, denying first McCulloch and then Connolly.
Newcastle had a rare chance after the break when Parker fired narrowly wide, and Emre hit the post with a low drive after 66 minutes.
It was the Turkey international's last contribution as he limped off with a recurrence of his hamstring injury.
Wigan were tearing through Newcastle at will, and Alan Mahon was guilty of an awful miss after 73 minutes, somehow failing to find the target from inside the six-yard box.
Roberts then headed an effort against the bar as it looked like their good work was going to go unrewarded.
But they made the deserved breakthrough with four minutes left as Roberts tumbled under a challenge from Elliott.
Connolly stepped up to coolly send Given the wrong way from the spot and secure a place in Saturday's fifrh round draw.
Wigan manager Paul Jewell:
"It was a tremendous display. We made life difficult for ourselves by missing so many chances.
"The game should have been over at half-time, and in some ways we are disappointed that it took a penalty for us to win it.
"We changed our shape but played some really good football. I told the players who hadn't been playing to go out and enjoy it and they certainly did.
"As I said, it should have been over by half-time, but at least we kept going."
Newcastle manager Graeme Souness:
"Overall we're not complaining - the best team went through. Our players didn't play near their potential.
"Our players say it wasn't a penalty but we can't complain because the best team won. It wasn't a good performance from us.
"The biggest thing we didn't do was start correctly and the initiative was given to them and we didn't get it back."
Wigan: Pollitt, Taylor, Jackson, Thome (Henchoz 30), McMillan (Baines 45), McCulloch, Teale, Skoko, Mahon, Connolly, Johansson (Roberts 69).
Subs Not Used: Francis, Bullard.
Goals: Connolly 88 pen.
Newcastle: Given, Ramage, Boumsong, Elliott, N'Zogbia, Bowyer (Brittain 45), Parker, Solano, Emre (Faye 71), Shearer, Luque (Chopra 57).
Subs Not Used: Harper, Clark.