The striker netted early in the second half, his third goal in as many games, to give the New Douglas Park side victory over Killie, only their fourth victory of the season.
It was the visitors who had looked the likelier scorers in an uninspiring first half on Saturday, but they were unable to find a way back after Offiong's ultimately decisive strike, substitute Donovan Simmonds squandering their best chance by firing well over from just five yards out.
Hamilton and Kilmarnock both made two changes to their starting line-ups.
Simon Mensing was suspended for the hosts following his red card in their last-minute draw at Dundee United and was replaced in defence by Martin Canning, who was returning from a ban; while David Graham appeared in place of the benched David Elebert.
Damien Rascle continued in goal for Kilmarnock after replacing the injured Alan Combe at half-time in the previous week's home defeat by Inverness, and Willie Gibson, a second-half substitute in that match, started in place of Allan Russell.
Kilmarnock came close to an opener after seven minutes.
following a free-kick in midfield, Gibson scampered down the left and floated a cross into the box which Simon Ford put just wide of the far post.
Gibson himself then went for goal after a Garry Hay free-kick, but his first effort from the edge of the area was deflected back to him and he put his second over the bar.
Kilmarnock continued to press as Hamilton failed to threaten at the opposite end, winning a free-kick just outside the left side of the area on 15 minutes, but David Fernandez headed over from Gibson's delivery.
Alex Neil's free-kick for Hamilton was then cleared to launch a counter-attack which saw Fernandez send in a diagonal shot goalkeeper Tomas Cerny dived to smother.
There was little in the poor second quarter to warm either set of fans on a freezing Lanarkshire day.
James McArthur had a half-hearted shot on target on the half-hour, but it never posed any kind of threat to Rascle, and Manuel Pascali glanced a header wide of the left-hand post from Jamie Hamill's cross.
Kilmarnock defender Frazer Wright was booked 10 minutes from the interval for a thumping challenge on James McArthur, but teenager James McCarthy squandered the subsequent free-kick.
Mark McLaughlin then headed straight into Rascle's arms while Kilmarnock finished strongly, with Fernandez releasing Craig Bryson for a burst down the right ending in Canning heading his cross clear.
It was Hamilton who finally opened the scoring six minutes after the restart, when David Graham's pass allowed Offiong to claim the ball inside the right corner of the penalty area.
The striker turned and shot, drilling a diagonal effort past the diving Rascle and into the bottom left corner for his third goal in as many matches.
It heartened Accies, who fashioned another opportunity minutes later from Neil's midfield free-kick, leading to a scramble in the six-yard box before the ball was finally cleared for a throw near the left corner.
Kilmarnock had a glorious opportunity to equalise just after the hour mark when Taouil's cross to the right-hand post found recently-introduced substitute Simmonds, but he contrived to blast his effort wastefully over the bar from no more than five yards.
The visitors tried beating a path upfield in search of an equaliser, with Gibson to the fore, but found themselves up against a resolute defence.
McArthur could have doubled Accies' lead just before the game entered its final 10 minutes, but after some good work in keeping possession and weaving in from the right to a good position in the box, he fired over the top-left corner.
Both teams had their share of possession in the closing stages, with play flowing up and down the pitch.
McCarthy made a good run for the hosts and, for Kilmarnock, Gibson fired a ball forward into the box but Cerny reached it well ahead of substitute Allan Russell.
Hamilton had to survive late scares when Gibson's corner flashed across the face of goal and when Ford shot into Cerny's arms in the fourth minute of added-time, but they clung on for the three points.