Scott McMann has challenged Hamilton to grasp the lifeline in front of them after Accies ensured their survival fate once again rests in their own hands.
Saturday's 2-1 win over St Mirren means Brian Rice's basement boys are now just three points from safety with two games remaining.
Hamilton's season has been blighted by injuries and Covid complications but their luck was finally in as Ross Callachan and David Moyo netted with fortuitous finishes to make sure Jamie McGrath's 16th goal of the season counted for nothing.
They now head to 10th-place Ross County a week on Wednesday before rounding off their relegation scrap against second-bottom Kilmarnock in a final-day shoot out.
The win in Paisley was Hamilton's first since mid-February but, having ended a miserable nine-game run without victory, skipper McMann is now targeting back-to-back results which will safeguard Accies' place in the top-flight for an eighth year in a row.
He said: "We know the next two games means it's in our hands. We need to win and we know what we need to do.
"The boys haven't felt unconfident through these last few weeks, we have always felt we've got it in us to win games.
"We got the rub of the green on Saturday with a couple of finishes and scored the goals we needed to.
"It sums up this club, it's that never-say-die attitude.
"I'd rather not be where we are but we have been here before and we can use it to our advantage and not panic.
"We'll focus on the games we've got. We went to Ross County before and beat them 2-0 so we have confidence we can do that again.
"The mindset is to win both games. Hopefully we can take this momentum into those games."
Saints boss Jim Goodwin gave Daniel Finlayson pass marks on his full debut despite his side failing to take the spoils.
The on-loan Rangers defender will make his move to Paisley permanent in the summer but it was a shaky display from the 20-year-old on his first professional start.
"Daniel has come on loan from Rangers mainly for us to have a look at him in training and to see how he got on alongside senior pros on a daily basis," explained Goodwin.
"He competes against Jon Obika, Lee Erwin, Kristian Dennis and Collin Quaner daily and does really well, so we felt it was the right time to give him his opportunity.
"I thought he did OK. He's still a young man and there's bits of his game that he needs to improve on.
"But overall I thought he had a decent performance."