The hosts had the better of an entertaining first half, with speedy forward Dan James denied by an excellent save from Newcastle goalkeeper Martin Dubravka early on.
Despite continuing in the ascendancy after the break Leeds, without injured striker Patrick Bamford, could not find a breakthrough, and their inability to make the pressure pay proved costly as Shelvey squeezed a 75th-minute free-kick home. Leeds threw everything at Newcastle late on, but they still could not apply the finishing touch as Marcelo Bielsa's side suffered their first defeat in three league games.
The victory was a crucial one for the visitors, who climbed to 18th in the standings, one point from the safety zone, having played one game fewer than Norwich City in 17th, and seven points behind Leeds in 15th.
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