The Jags were trailing 2-1 at Central Park after a Craig Moore double either side of a Steven Lawless leveller put the Blue Brazil on course for the victory.
But their blushes were spared with just 20 minutes remaining as referee Craig Charleston called a halt to proceedings after a thick freezing fog enveloped the stadium.
Conditions had been getting worse since kick-off and the whistler consulted with interim Jags boss Archibald and his Fife counterpart Colin Cameron 10 minutes into the second half but decided to carry on.
The game soon became a farce, however, with fans unable to see the ball and the opposite side of the pitch obscured from view.
The call-off leaves Thistle with two games in hand over Irn-Bru First Division title rivals Morton, but with few free midweek slots to come they face a congested final few weeks of the campaign.
Archibald said: "You couldn't really see the other side of the pitch.
"It wasn't ideal right from the word go but we were keen to get the game going. He [Charleston] came over and asked us the first time and I think that was on the back of the Cowdenbeath punters shouting that they couldn't see.
"He came over but myself and Colin said we wanted to play.
"Our fans must have started shouting and it has added to it as well.
"You can't blame him. It was bad, you couldn't really see. It didn't get any worse, it might have if we had continued.
"The vision was like that in the first half, you couldn't see the other side of the pitch.
"It is not ideal for us, we are going to have backlog of games now. We were 2-1 down with 20 minutes to go so we will take it."
He went on: "I have no idea when we will fit it in.
"That is why we were keen to get the game on.
"It just means we need to come back here again and win."
The dramatic call to abandon the tie may yet prove beneficial to Thistle, with the Jags now given another chance to claim all three points at Central Park after their two previous trips through to Fife were postponed due to frozen pitches.
The Firhill side were never at their best but responded well to losing an early goal and levelled through a Lawless strike before falling behind again.
It was all to prove worthless in the end but Archibald was still dismayed with a sloppy showing.
He said: "I wasn't happy with the performance. We had five or six chances in the first half but I wasn't happy with the way that we started.
"We then got into the game and started creating chances.
"I wasn't happy with the back four or the way we defended.
"It is a lottery here, one long ball and you are in.
"That was disappointing but, going forward, we created four or five chances in the first half."