Substitutions, particularly those made late in a game, can go either way but on this occasion they paid off spectacularly. Having watched his callow side pummel Dundee for much of this match, his frustration mounting with every chance spurned, McGlynn's final move was to throw on John Sutton and Arvydas Novikovas with five minutes remaining in a desperate attempt to break the stalemate.
Within seconds, he was rewarded. The Lithuanian winger scampered clear down the left and his flashing cross was directed past Rab Douglas by Sutton's head.
It was the least that Hearts deserved, and revived their ambitions of gilding a place in the Scottish Communities League Cup final with a top-six finish, even if McGlynn was reluctant to accept praise. "Yeah, they linked up well," was his modest response. "We had to try and win and, had it not been for Rab, we could have had three or four."
McGlynn, instead, was more minded to garland his players, none more than Billy King. Making his debut on the right wing, the 18-year-old demonstrated an eagerness to accept the ball in tight spaces and an admirable composure, the lack of refinement in his decision-making countered by his desire to burrow into dangerous areas. Indeed, as early as the second minute King scampered along the perimeter of the Dundee box before dragging an effort wide, then was unfortunate that a wickedly dipping drive cleared Douglas' crossbar.
With Michael Ngoo a reliable reference point, Hearts were able to establish a beachhead in the Dundee half and, although they struggled to cleave open their visitors, the vagaries of the blustery wind combined with their territorial advantage to ensure several sights of goal. Jamie Walker, who had already tested Douglas with a header, forced the veteran goalkeeper to fling himself to his right to push a fierce, angled shot past a post and perhaps should have scored when an Ngoo shot squirted in to his path a couple of yards from goal, only for the combined effort of Douglas and Gary Irvine to thwart him.
Although marshalled relatively well by Declan Gallagher, Ngoo still caused problems for Dundee and came closest to opening the scoring. The towering Londoner soared above Colin Nish to meet a King cross six yards out but his powerful header scudded against his marker's back and fizzed over the crossbar.
The change of ends at the interval did little to stem the flow. Hearts howled for a penalty when Walker's acrobatic effort – again a consequence of Ngoo's mischief making – appeared to strike Irvine on the hand, then Holt rattled an audacious effort against the frame of the goal.
King, however, was culpable of spurning Hearts' clearest opportunity just before the hour. Having managed to wriggle in to space on the byeline, Jason Holt picked the teenager out in front of goal but, despite taking a sound touch, the debutant dragged his shot wide from eight yards. A further effort by King, a few moments later, was on target but Douglas made the save.
The goalkeeper would eventually be beaten by Sutton, but did at least prevent matters becoming worse with another splendid stop from Walker in stoppage time. "Rab seems to keep his best performances for games against us," McGlynn said.
It was one of the few positives Dundee could derive from a frustrating evening. Barry Smith selected an attacking team, boasting two strikers, a couple of wingers and the playmaking talents of Gary Harkins – who made his second debut for the club – but the visitors toiled to even get out of their own half for much of the evening. Given that they had scored just six times in 12 away matches this term, such struggles were not entirely surprising, even if a staggering 43% of the points amassed by the Dens Park side prior to last night were at the expense of Hearts.
Dundee's only genuine sight of goal in the entire contest fell to Nicky Riley, who lashed wildly over the frame of the goal after meeting John Baird's searching deep cross. That it was not to be their night was confirmed when victories for both St Mirren and Ross County extended the gap between the Clydesdale Bank Premier League's bottom side and safety to 14 points with just 14 games remaining.
Given they have now gone 10 league games without a win, the situation appears bleak but Smith refused to entertain suggestions that his side's survival hopes were forlorn. "We can only concentrate on getting points ourselves," said the manager, whose attempts to sign a Dutch striker fell through yesterday. "We handled them relatively well but we've got a young back four and they got the breakthrough in the end."