The striker took his tally to five for the season with an excellent individual goal in 78 minutes, but was then sent packing by referee Stephen Finnie for foolishly kicking the ball away in the last minute of normal time.
Offiong will now miss the visit by Inverness Caledonian Thistle in a fortnight's time.
Hamilton deserved to take the points on a freezing cold January afternoon, but Aberdeen contributed mightily to their own downfall by turning in a simply lacklustre performance.
Aberdeen started strongly and in just seven minutes Jeffrey De Visscher was unlucky to see his angled drive punched over by Tomas Cerny.
Hamilton passed up a decent chance two minutes later when Brian Easton and James McCarthy linked up well down the left to set up Offiong, but the striker stabbed his effort over.
The impressive Scott Severin sent a 30-yard free-kick over in 18 minutes and ten minutes later a free-kick was knocked down by Gary McDonald to Darren Mackie, but the Aberdeen man failed to control and the chance was wasted.
Hamilton forward David Graham was unlucky not to score in 37 minutes when he picked up a loose ball on the right of the box, but sent a scorching drive just past the left post with Jamie Langfield beaten.
Aberdeen nearly made the perfect start to the second half when a defensive error let De Visscher in, but he volleyed past from a good position.
Hamilton grabbed the opener from the spot when McCarthy was brought down in the box by Zander Diamond and Simon Mensing clinically rammed the ball home after 51 minutes.
Accies nearly gifted Aberdeen an equaliser in 55 minutes when Mark McLaughlin's attempted back-header landed in the path of Lee Miller, but the striker's header was superbly palmed round the right post by Cerny.
Two minutes later Cerny brilliantly punched a Miller free-kick over.
Mackie should have pulled his side level in 73 minutes, but somehow headed a De Visscher cross past from almost point-blank range.
Three minutes later Graham went close for Hamilton again, but saw his low, angled shot parried by Langfield, with the ball hacked away from Offiong.
But Hamilton sealed the points in 78 minutes when McCarthy's flick-on released Offiong, he controlled superbly and drilled a low shot across Langfield and into the bottom right corner.
Offiong should have scored a second in 81 minutes when he mugged Severin in the box, but after drawing Langfield, he sent a low shot inches past the left post.