Perhaps they thought it was all over? Gavin Rae, upon being accosted by one of a few hundred fans who had darted on to the plastic, shook his head and grimly wondered what his side's supporters were up to. This league, which has twisted and turned all season, is far from won.
"I'm not really sure how I felt about that," Rae winced. "I appreciate their support, they turned out in their numbers, but nothing's done yet."
While it was certainly tempting fate, few could blame Dundee's travelling support for getting a little carried away. Only a week after these same faces trudged out of gloomy Cappielow certain the dream was over, just about everything possible went right for their club during the course of a sunny afternoon in Alloa.
They would score, then Dumbarton scored; Morton equalised against Falkirk, and Dundee scored again, then Alex Neil was sent off at the Bet Butler Stadium. And when Craig Beattie gets a goal you know it is going your way.
It was a giddy crescendo of right good things happening, one after the other, building and building to the final whistle where it spilled out on to the pitch with a thousands-strong wail of joy and disbelief. The visiting support far outnumbered the home at Recreation Park, and the consistent bursts of roaring spurred on the players to a priceless victory. A draw at home to Dumbarton next week will now be enough, barring a nine-goal victory for Hamilton Academical.
Paul Hartley, the Dundee manager, had dropped Craig Wighton to the bench in favour of Christian Nade, and was rewarded by a brutish performance. Wighton is promising, and the future of the club's front line, but Nade was simply a walking brick that Alloa Athletic's black and gold shirts buzzed around to no avail. He swatted away their attentions, apart from at one moment when he lay clutching his head, prone as his team's physio sprinted on. In the process of clattering Graeme Holmes, though, the big man had opened the scoring.
Barry Smith, the Alloa manager, was unhappy with the second, arguing that the penalty - awarded when Nade headed the ball on to the already booked Daryll Meggatt's hand - should have been punishment enough. "I don't think it's a booking, he's had very little time to react, the ball's hit him," he said. "The sending-off was a double whammy."
Peter MacDonald converted confidently and celebrated furiously. He later smacked a ripping bicycle kick off the bar; the metal shuddered.
The points, by then, were already won and Alloa were left to rue a missed chance early in the first half. Holmes had darted through from deep but Kyle Letheren was quickly out to block the attacker's lob.
A final word from the Dundee manager for his former club, which could plummet to a relegation play-off? "We're focused on what we do," Hartley said. It was clear he meant it.