Just after the hour mark, having watched their sides both miss a host of chances, Paul Hartley and Tommy Craig brought on strikers. Both players - Peter MacDonald and Stephen Thompson - were crowd favourites, greeted by big cheers. Both were told to win the game.
St Mirren's Thompson, though, hadn't played since the start of May. MacDonald, on the other hand, had been left restless on the bench, fit and firing, but out of the side and bristling. If he had a point to prove, he proved it.
The ball was cleared out of the St Mirren area. There was no danger but, as everybody traipsed back toward the halfway line, it was unexpectedly hoofed back long by Paul McGowan. MacDonald was the quickest to turn and darted on to the high, spinning ball. With a marvellous first touch - and just onside - he drove towards goal and finished cleanly beneath Marian Kello. In the 80th minute, it was decisive.
"His touch was fantastic to take it forward, the calmness to put in the bottom corner but we know he can do that," said Hartley, his manager. "Sometimes you have to grind a result out and we did that. We're a great addition to the league. We're undefeated in five, we're hard to beat."
The match was remarkable for its number of wasted efforts. Early on, Kenny McLean was sent through by Callum Ball, who drove a low cross-field ball into the St Mirren midfielder's path. A good touch but a shanked shot followed. Then Adam Drury's drive was blocked into the path of Jason Naismith, who drilled low towards the bottom-left corner. Kyle Letheren just tipped it wide.
Drury - just signed on loan from Manchester City - missed a golden chance, volleying over. He was given a warm round of applause before kick-off and when he was taken off, but lacked sharpness, though one dart to the line and cross late in the first half brought the crowd to their feet.
Perhaps the worst offender when it came to spurned opportunities was Dundee's Gary Harkins. Completely unmarked on the left-side of the area, he waited and tried to jink inside rather than shoot quickly.
St Mirren could consider themselves unfortunate not to take anything from the game. "We just cannae put the ball in the back of the net," said Craig. "It really is a sore one."
Thompson and MacDonald both worked the goalkeepers as they chased a winner. The latter drove in a shot that was palmed away and then scrambled to safety. About a minute later it was Thompson's turn, but he could not generate enough power to beat Letheren. Then Craig Wighton went down in the St Mirren box and the away fans cried foul, but referee John Beaton shook his head.
As they tried to get back into the game late on, St Mirren drove forward and the best chance fell to Thompson. Free at the far post, he could only play it into the goalkeeper's arms.
Minutes earlier, as MacDonald celebrated his goal, his manager had screamed at him to grab his attention. The substitute glanced over towards the touchline to be met by a curt nod and a thumbs up. Job done.