The Maryhill club - in their first season back among Scotland's elite - secured their top-flight status for another year after a compelling 4-2 win at Tynecastle.
Thistle had looked like needing something from their final game of the season against Ross County on Saturday after twice going behind to Callum Paterson and Danny Wilson goals at Tynecastle.
But Lyle Taylor and Gary Fraser cancelled out those efforts, with Lee Mair and Kallum Higginbotham wrapping up the victory.
The result lifts Partick up to seventh place and they can now enjoy Saturday's match as Hibernian and Kilmarnock do battle to avoid the relegation play-off place.
Archibald said: "It's bigger than anything I've done as a player; the lads have been a credit to themselves.
"It was a massive relief, the first emotion is relief. I'm just glad to get over the line because I don't envy those managers that are involved in it.
"It's hard to put into words what it means to stay in the league, I've been here through relegations and it's horrible, it affects everybody at the club and it affects everything you do.
"It's massive and I think the fans deserve it at this club."
Partick inflicted relegated Hearts' first defeat in seven games but manager Gary Locke, whose side finish the season away to St Mirren on Saturday, was
philosophical about the loss.
He said: "Credit to Partick, they deserved it. They played really well in the second half and battled really hard.
"You could see by their reaction at the end they were delighted.
"We are disappointed to lose but in the main I think the players deserve enormous credit, they have been fantastic over the last couple of months."