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Newcastle finished the first half strongly, as Mathieu Debuchy twice found gaps in the defending champions' defence to test David de Gea in stoppage time, but the keeper made a pair of solid saves to keep the teams level at the break.
Javier Hernandez also tested the visiting keeper shortly after the restart, but once again Krul was able to make the save.
David Moyes's men continued to look the more likely to break the deadlock as Patrice Evra struck the post with a header before Van Persie, Hernandez and Nani all tried to reach the rebound, but Krul managed to gather in the penalty box scramble.
Van Persie thought that he had scored the equaliser for the Manchester side 10 minutes later as the striker headed in from a free kick, but his effort was ruled out for offside.
Wilfried Zaha came off the bench to provide a late threat for the hosts but his attempt at the far post went just wide, while Van Persie fired another free kick off target.
The home side continued to push into stoppage time, but Newcastle made sure that they had numbers back to protect their lead, making it five wins in their last six matches.