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Wolves tossed away a two-goal lead before Ndah booked their place in the fourth round with a 50th minute strike.
Dave Jones' side may be struggling in the First Division, but they were more than a match for Premiership high-flyers Newcastle.
Wolves could not have made a better start as Paul Ince fired them into the lead after just six minutes following a well-worked corner routine.
Mark Kennedy collected his short corner back from Shaun Newton and then sent over a centre that was headed across the goal by Paul Butler into the path of the on-rushing Ince who volleyed home from ten yards.
Wolves were dominant in the opening exchanges and could have increased their advantage before Kennedy fired them further ahead in the 29th minute.
Butler and Colin Cameron, who was denied by a smart save from Shay Given, both went close before Kennedy struck.
The Republic of Ireland international swept home a low drive at the far post following a right wing cross from Cameron.
Kennedy threatened to grab Wolves a third when he headed into the side netting 60 seconds later.
But it was that let-off that finally sparked Newcastle into life and they stunned Wolves by pegging them back on level terms with two goals in two minutes at the end of the first-half.
Craig Bellamy created the first, crossing for Alan Shearer whose 40th minute snap shot was beaten away by Butler only for rebound to fly to straight to Jermaine Jenas who nodded the ball into an unguarded net.
Wolves were still reeling from that setback when United drew level from the spot.
Referee Rob Styles had no hesitation in awarding a penalty after Wolves centre half Joleon Lescott pulled back Bellamy after the ball had been cleared.
Shearer comfortably beat Matt Murray from the spot, sending the England under-21 international the wrong way.
Lescott made amends for giving away the spot-kick in a frantic start to the second-half.
He twice cleared off the line in the space of a few seconds, first blocking a free-kick from Shearer and then beating away the follow up from Clarence Acuna.
The value of his intervention became apparent just a minute later when Ndah fired Wolves back into the lead after 50 minutes.
Once again, Newcastle were undone on the flanks. Kennedy floated over another cross that Newton headed back into the path of Ndah who was able to stab home his shot from two yards.
While Ndah's strike clinched their success, Wolves still had to ride their luck before clinching their triumph.
Murray rescued Wolves by denying Bellamy after 74 minutes before left-back Lee Naylor cleared off the line two minutes later from substitute Lomana Lua Lua.