Bobby Wales scored his first Kilmarnock goal in added time to set up a winner-takes-all second leg with Tromso in the Conference League third qualifying round.
Kilmarnock had led early on through captain Kyle Vassell, but Tromso turned the match on its head thanks to goals from Jakob Napoleon Romsaas and Lasse Nordas.
Prior to Wales' dramatic leveller, Kilmarnock had been awarded a penalty when Joe Wright was clattered by goalkeeper Jakob Haugaard but referee Menelaos Antoniou overturned his decision following a video assistant referee (VAR) intervention.
It was up to 19-year-old Wales to save the day in the 92nd minute, sweeping home a loose ball from a corner to send Rugby Park into raptures.
Whoever progresses will play Copenhagen or Banik Ostrava in the play-off round, with the Danes leading 1-0 going into next week's second leg in the Czech Republic.
It took Kilmarnock just six minutes to hit the front. Liam Polworth's cross was glanced on to the post by Liam Donnelly. It seemed the Tromso defence had time to clear, but Vassell slid in to stun the Norwegian visitors.
Unfortunately for the hosts, that was the best of the first-half action. Tromso recovered well and Robby McCrorie was forced into a good save to deny Jens Hjerto-Dahl.
Five minutes into the second period, it was all-square. Kilmarnock failed to clear twice, giving away the ball on the edge of the box, and Romsaas was slipped through by Nordas before tucking home.
Then came the first moment of controversy. Fraser Murray, on as a half-time substitute, was charged into by Velte Skjaervik. No penalty was given, and the VAR did not intervene.
Tromso added to Kilmarnock's sense of injustice by taking the lead. Hitting on the break, they cut the hosts apart too easily and Nordas was able to power into the box and drill a low finish into the far corner.
Then, the penalty came. Sort of. Wright was cleaned out by Haugaard, who had come out to punch away a cross. Antoniou pointed to the spot for what seemed a pretty open-and-shut case, but the VAR screen soon beckoned and the decision was overruled.
Kilmarnock responded well from that disappointment. Stuart Findlay should have netted when he got on to the end of a deep free-kick, but he was offside anyway.
The pressure was building though, and it told in added time. A corner from the right bobbled in the box and Wales scuffed the ball home.
Player of the match - Bobby Wales
Killie rescue draw from jaws of defeat - analysis
Kilmarnock's grit is well known to Scottish football fans, but this comeback was still one of the more surprising ones in Derek McInnes' catalogue.
Tromso did not exactly dominate in large spells but they seemed more comfortable in possession and slightly more threatening.
Another surprise to Kilmarnock fans might be how soft the two goals they conceded were, extending an unwanted recent trend.
Both of Cercle Bruges' goals in the Europa League loss that put Killie into the Conference League were avoidable. And while other teams will ship four goals at Celtic Park this season, McInnes would have been irritated by the manner of Sunday's 4-0 Scottish Premiership defeat.
Tromso's first goal was entirely preventable - a goal of Kilmarnock's own making as they failed twice to just boot the ball away or show some composure to keep their foot on it. That soft centre needs addressing, and quickly.
But yet, come back they did. All to play for in the north of Norway next Thursday.
What the manager said
Kilmarnock manager Derek McInnes: "We're up against a good team. We tried as best we could. We lost a wee bit of confidence when they started to make a few passes. We needed to be better at looking after the ball when we won it.
"I thought we should have had a penalty. I don't see why that's overturned. I've seen it again, [Jakob Haugaard] might get a little fraction of the ball but he's careered into Joe [Wright] with his fist. I'm surprised that's been overturned, the referee's decision was the right one.
"What a brilliant moment for [Bobby Wales]. He's doing really well. I love the kid, he's somebody who is going to do so well in his career. We want that to be here with us. It was fitting the way we finished the game."
What's next?
Kilmarnock face St Johnstone on Sunday (15:00 BST) in league action before travelling to Tromso next Thursday (18:00).