Persistance paid off for the Ivorian, who had previously had three unsuccessful attempts in a 45 minutes dominated by the hosts at the Liberty Stadium.
Bony's first opportunity came on six minutes, when he glanced a header from a corner past the post, but Kasper Schmeichel was tested by his next effort - a 20-yard shot which the Dane held well in the centre of goal.
A smart turn on the edge of the box provided him with the space to try his luck again with a wide left-footed drive, but he soon did get his name on the scoresheet following a smart combination with Gylfi Sigurdsson.
The Icelandic midfielder dummied for Bony, who turned the ball around the corner for his teammate before continuing a run which Sigurdsson spotted, and Bony supplied a bending finish beyond Schmeichel from 12 yards.
Nobody has more top-flight assists than Sigurdsson this season, but Swansea's supplier should have had a goal of his own when Schmeichel's scuffed pass went straight to him. Visiting captain Wes Morgan reacted rapidly to fairly poke the ball from him before Sigurdsson could set himself to shoot.
Leicester manager Nigel Pearson recalled Riyad Mahrez, David Nugent and Jamie Vardy in a bid to find a first away goal in three matches, but they failed to fashion the Foxes a single chance before the break.