Newcastle suffered a seventh consecutive loss to raise fears of relegation.
Ayoze Perez gave the home side the lead after 20 minutes, slotting home Emmanuel Riviere's pass following Swansea defender, Jordi Amat's mistake.
The Swans equalised in first half stoppage time through on-loan striker, Nelson Oliveira, who headed past Tim Krul direct from a corner.
Second half strikes from Glyfi Sigurdsson and Jack Cork gave Swansea a comfortable 3-1 lead before Siem de Jong, making his first Newcastle appearance since August, grabbed a late consolation.
Newcastle stay in 14th, but are now just five points above the relegation zone. Swansea remain in 8th.
NEWCASTLE: Krul; Janmaat (Abeid, 61), Williamson, Coloccini, Anita; Colback, Taylor, Gutierrez, Cabella (de Jong, 74); Riviere (Armstrong, 74), Perez. Subs: Woodman, Gouffran, Obertan, Ameobi.
SWANSEA: Fabianski; Rangel, Fernandez, Williams, Amat; Cork, Shelvey, Dyer, Sigurdsson (Emnes, 81), Montero (Grimes, 69), Oliveira (Ki, 72). Subs: Tremmel, Britton, Bartley, Fulton.
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