The visiting team led on 22 minutes when Mohamed Diame scored at the back post after Kenedy's corner was flicked on by Ayoze Perez.
Palace missed two great chances to equalise before half-time.
Wilfried Zaha was denied by a DeAndre Yedlin block and Christian Benteke failed to convert an open goal.
Ciaran Clark's shirt-pull on Benteke won a penalty that Luka Milivojevic converted in the 55th minute.
James McArthur, Yohan Cabaye and Benteke all came close to winners for Palace but Newcastle stood firm, with Clark blocking two efforts on the goalline.
Palace are 14th on 27 points, two places and two points above Newcastle.
Crystal Palace: 10 Feb v Everton (A)
Newcastle: 11 Feb v Man Utd (H)