Accies now hold their Premiership destiny in their own hands after clambering their way to a 2-1 win over St Mirren in Paisley.
Two fortuitous finishes from Ross Callachan and David Moyo were the lucky break the basement boys have been hoping for after a season spent battling injuries and Covid complications.
The goals provided Rice's team with their first win in ten games and means they are now just three points from safety.
They are also no longer relying on favours from elsewhere as they prepare for two momentous final games away to tenth-place Ross County a week on Wednesday ahead of their final-day shoot-out with second-bottom Kilmarnock.
Hamilton have beaten the drop in each of the last seven seasons but given what they have been through this campaign, Rice reckons this would be the biggest escape act yet.
"It would be like climbing Everest with your flipflops on," said Rice, who watched from the SMISA Stadium stands as he began a two-game touchline ban. "It would be the biggest achievement I've ever achieved with what we've been through this season.
"I'm absolutely delighted to come and win. It's massive. I said yesterday we need to do what we need to do then look at the situation. It's going to go down to the last game.
"Everyone gave full effort. People throw their bodies on the line every week and that's what we need.
"It's not belief into the squad I need, it's getting my quality players on the pitch that's been the problem. My flair players have all been injured but I can't ask for any more than what I got."
Buddies boss Jim Goodwin was hoping to give key men Conor McCarthy and Jamie McGrath the afternoon off ahead of next week's Scottish Cup semi-final with St Johnstone.
But an injury to Marcus Fraser in the warm-up meant defender McCarthy was forced into action from the start while McGrath grabbed his 16th goal of the campaign after being thrown on in the second half in a bid to turn the game around.
On-loan Rangers youngster Daniel Finlayson was handed a chance to impress alongside fringe men Cammy MacPherson and Collin Quaner.
But Goodwin said: "I gave opportunities to one or two who had been champing at the bit to start but they haven't done themselves justice or given me a headache for next week.
"The players have been fantastic and we won't be too hard on them. We'll reiterate we can't play at 60 per cent because if you do, you get beat.
"If we don't play at full tilt against St Johnstone we won't get the result."