Scott Parker gave Newcastle a 54th-minute lead, and that should have been enough, but for individual errors by first Peter Ramage and then Titus Bramble.
Chris Coleman: "I have got to be honest, to come away with three points on the balance of the game, you have got to say Newcastle have been unlucky there and we have been a bit fortunate.
"I would have been happy with a point, but to go back with three is fantastic."