The English striker took his tally to four for the season with a well-taken strike seven minutes into the second half at home to Kilmarnock.
That goal was pretty much the only excitement on a bitterly cold afternoon at New Douglas Park, but Killie will rue at least one glaring miss.
It wasn't a match with an abundance of free-flowing football, but both sides defended well in patches, while the midfield battle was where the game was won and lost.
Killie looked the better side early in the game and Willie Gibson's cross from the left was headed narrowly past the right post by Simon Ford after just seven minutes.
The next moment of note came 13 minutes later when Mehdi Taouil played David Fernandez through on goal, but the Spaniard's effort was comfortably dealt with by Tomas Cerny.
Hamilton 's first shot on target arrived in 31 minutes when James McArthur went on a mazy run, but Damien Rascle was equal to his low shot.
Mark McLaughlin met Alex Neil's free-kick with a looping header in 39 minutes, but Rascle wasn't troubled greatly.
Hamilton came out for the second half with their tails up and David Graham fired over from a good position after 49 minutes.
But it was Graham's ball two minutes later that released Offiong on the right, he drew Rascle and slammed the ball home into the bottom left corner.
Kilmarnock should have levelled in 62 minutes when Frazer Wright's pass picked out sub Donovan Simmonds, but he somehow blazed over from four yards out, with the goal at his mercy.
James McArthur could have doubled Hamilton's lead after 78 minutes when he found himself in a good position on the right, but sent his angled shot high and wide.
But Cerny ensured that Accies kept the points with an instinctive block from Ford, which summed Kilmarnock 's day up really.
Hamilton celebrated after the final whistle and well they might as this result, coupled with St Mirren's 2-0 defeat by Dundee United, takes them up into 11th spot.