Amad Diallo scored his first Premier League goal to put the hosts 2-1 up in the second half, before Rasmus Hojlund came off the bench to wrap up the points.
Newcastle were rewarded for a bright start to the second half as Gordon met Jacob Murphy's cross to fire an equaliser past Andre Onana in the 49th minute.
Less than 10 minutes later, though, Eddie Howe's side were behind once more - Diallo latched onto a poor clearance to rifle a powerful strike past Dubravka from the edge of the box.
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