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The home side threatened in the early stages as Wayne Routledge raided down the left and hit a cross to the back post that evaded the head of Bony. However, the ball fell to Nathan Dyer, but he scuffed his attempted volley.
Swansea were dominating possession and Gylfi Sigurdsson tested the handling abilities of Saints keeper Fraser Forster with an effort from distance, but the England man made a comfortable save.
Garry Monk's side came within inches of taking the lead as Sigurdsson released the run of Routledge down the left who raided into the box, but his right-footed shot cannoned off the bar and went over.
The home side continued to threaten and went closer still when Bony rose highest in the penalty area to power Sigurdsson's corner at goal, but his header was cleared off the line by Ryan Bertrand.
Swansea were reduced to 10 men just before the break when Bony was given a second yellow card for a reckless challenge on Maya Yoshida as he hacked the defender down from behind.