The hosts had taken the lead with their first goal for four games, but were pegged back in the dying moments of the half.
Swansea started the game well, controlling possession and pressuring the Newcastle defence throughout the opening 20 minutes.
Pablo Hernandez was a particular threat, combining with Angel Rangel and firing across the six-yard box before delivering for Bony at the near post, only for Tim Krul to deny the striker.
It was the hosts who took the lead, though, somewhat against the run of play, as Shola Ameobi bundled his way into the box and fired the ball into the bottom corner.
Swansea increased their intensity in search of an equaliser but it was Newcastle who threatened again, with Ameobi bursting into the box in similar circumstances, only to see this effort blocked by Jordi Amat.
There was a substitution after 32 minutes, however it was among the officials. Chris Foy, who had taken an earlier blow to the head from the ball, needed to be replaced by Anthony Taylor.
Newcastle were then forced into their own substitution as Loic Remy was put back into action earlier that expected after Luuk de Jong picked up an injury as the half drew to a close.
Just as the Magpies were looking forward to a half time lead though, Bony found space and nodded in Ben Davies's cross from close range.