Hamilton's Simon Mensing was sent off midway through the second half for a second bookable offence.
Accies took the lead through Simon Mensing with Martin Canning seemingly in an offside position.
Offiong met Simon Mensing's back-post cross but could only head tamely into the arms of Balogh.
Simon Mensing missed an 80th-minute penalty for Hamilton to sum up the Lanarkshire side's miserable afternoon in the capital.
But, fortunately for the SPL newcomers, Simon Mensing was on hand to clear the loose ball off his line.
Michael Duberry handled inside the Saints box from a corner and Simon Mensing converted the spot-kick with 22 minutes remaining.
Derek Lyle and Simon Mensing went close for Hamilton in the second-half but they could not find a way back.
Simon Mensing tried his luck for Hamilton in the opening minutes with a powerful strike which curled narrowly wide of Ma-Kalambay's post.
St Johnstone took a first-half lead through Sam Parkin's header, then Simon Mensing equalised for Hamilton from the spot with 22 minutes remaining.
Simon Mensing rose above goalkeeper Allan McGregor to meet a Neil corner and his header thumped off the face of the bar from four yards.
Then Rooney got beyond Simon Mensing for the first time in the match and had an effort on goal, but Graham headed clear to concede a corner.
McGregor used a hand to prevent Simon Mensing's shot crossing the line and was shown a red card before Stevenson sent Hutton the wrong way from the spot.
Brendan McGill had opened the scoring for the home side just before the break, with Simon Mensing heading the equaliser from a Derek Lyle cross early after the break.
With five minutes on the clock Gallacher mis-hit his kick straight to Simon Mensing, who passed to the Accies midfielder who somehow knocked the ball wide from just a few yards out.
BBC: Alex Neil (r) and Steven Thomson in action at St Mirren Park
Flavio Paixao ought to have scored when Simon Mensing found time and space down the right to pick out the Portuguese forward, but he skewed his shot a few inches past Allan McGregor's post.
Hamilton had the best chance of the game thus far when a Stevenson header was won in the air by Simon Mensing, who knocked the ball onto Offiong, but the striker failed to keep his header under the bar.
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