Accies have yet to record their first victory in six outings under player-manager Martin Canning while Kilmarnock have won only twice in 15 outings.
The visitors were happier with the outcome, of course, having lost manager Allan Johnston on the eve of the match.
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His assistant, Gary Locke, will be in charge for the remainder of the season and he will be throwing his hat into the ring when it comes to deciding on Johnston’s successor.
“It’s been a difficult couple of days because Allan wasn’t just the manager, he was also a close friend of mine,” he said.
“He made a decision on Thursday which surprised us all but the reason I’m sitting here now is that he told me to try and take this opportunity. I wouldn’t be doing that without his blessing.”
Hamilton engineered the first clear-cut opening after 16 minutes when Danny Redmond played Jason Scotland in on goal.
The former Trinidad and Tobago striker feinted to send Manuel Pascali the wrong way but spoiled it all by driving over the bar from 10 yards.
Kilmarnock then had a reasonable claim for a penalty when Martin Canning sent Tope Obadeyi sprawling but, although Accies’ player-manager was booked for the foul, referee Alan Muir deemed it to have taken place just outside the area.
More typical, though, was the fine diving save from Samson to deny Redmond, whose low shot from Ali Crawford’s through ball had looked a certain goal.
Yet Accies failed to capitalise on their first-half superiority and it was the visitors who looked more threatening after the interval.
Josh Magennis was inches away from breaking the deadlock with a header from Chris Chantler’s cross which beat Michael McGovern but drifted wide of his left-hand post.
However, the pivotal moment arrived 14 minutes from the end when Louis Longridge’s long ball played in Danny Redmond only for Manuel Pascali to bring him down from behind.
“The lad’s come straight through the back of me,” said Redmond. “I couldn’t believe it when I turned round and there was no flag or whistle.
“I’m through on goal, so why would I go down? But that’s football. I don’t know what the referee and linesman thought they saw but I’m disappointed.
“The referee told me he’d been on the halfway line and couldn’t see it and the linesman told him the defender had touched the ball but I didn’t fall over on purpose – he came through the back of me but that’s life.”
Pascali saw it rather differently. “I’d need to see it again but I thought I got the ball,” he said.
“I was worried because I was harshly sent off at Parkhead and I didn’t want that to happen again.
“But there were also a couple of times when we might have had a penalty. It was important for us not to lose the game.
“I played with Gary in my first season here and he brings some fresh air and some positivity. He can have a laugh but he also works hard.”