Peter MacDonald converted the winning goal on 86 minutes, capitalising on defensive hesitancy by Ismael Bouzid to prod the ball beyond his namesake Jamie in the Hearts goal. Many suspected Jefferies would guide his side to the latter stages of this competition, some believed they harboured the potential to lift the trophy given their imperious league results. They were certainly strong favourites to dispense with St Johnstone, so this result will be filed under "mild cup shock".
If Hearts had to endure a reminder of the fickle nature of Scottish football following their breathtaking form of late, better it occurred in the Scottish Cup than the SPL. That might be a popular view amongst Tynecastle regulars today but this was nonetheless a sore, not to mention surprising, reverse for Jefferies and his staff, especially since it brought an unbeaten run of nine games to an end.
Not that the visitors did not deserve to progress. MacDonald's goal secured his club's place in the fifth round against Falkirk or Partick Thistle, their reward for an intelligent performance which centred around stifling Hearts before hitting them with a classic late sucker punch. The gameplan was the brainchild of manager Derek McInnes.
St Johnstone emerged only occasionally from their shell in the first half and became slightly more adventurous after the interval as the minutes ticked on with the scoreline goalless. David Obua wasted a glaring opportunity to put Hearts ahead midway through the second period, scooping Stephen Elliott's delivery over the crossbar from around five yards when it seemed easier to score.
That moment of profligacy imbued those from Perth with belief that they could snatch victory. When Bouzid headed a cross ball into the air four minutes from time, Murray Davidson nodded it back into dangerous territory. Bouzid pursued it but hesitated, MacDonald arrived only for the ball to ricochet off his shin and inadvertently out of the centre-back's reach. All that was left was for the striker to slot into the corner of the net.
"It's hard to go over the top and criticise," said Jefferies. "When you look at some of the players who were outstanding recently, they never performed anywhere near that level. Particularly in the middle of park, but all over we weren't as good as we have been and we paid the penalty for that. St Johnstone, in the second half, always looked like a goal could come from them.
"We got the best chance at 0-0 when David Obua put the ball over the bar. I don't know how he's done it. It was probably harder to put it over the bar. That was a chance that might have meant a different outcome in terms of going through.
"The way goal was scored was a catalogue (of mistakes). We couldn't clear it from the edge of our own box, then it was played in behind us. I think we had a chance to clear it and Ismael miskicked it. The boy (MacDonald) was as surprised as anybody that it landed at his feet. Then he's sclaffed it and it's gone in the corner. We've got no complaints. St Johnstone deserved to win because they were always looking more threatening in the last third. We were guilty of bad decisions and bad passing. Even headers which we should have been pulling down were being headed back to the other team.
"We always said that somewhere down the line we were going to lose. The disappointing thing is I hoped it would be on a day when we'd given our all, played well and it wasn't our day."
Hearts made the early running in a game played out in an atmosphere quite surreal for Tynecastle. Normally a venue synonymous with raucous crowds, the closure of the Wheatfield Stand diluted the effect of the stadium's unique acoustics. On the field, the home team were striving admirably to rouse their followers. Arvydas Novikovas delivered some fine early balls in addition to a marauding run and cross on 17 minutes which no-one in maroon gambled on.
In between, Ryan Stevenson drove a low shot wide against his former club.
Kevin Kyle was embroiled in a fascinating physical contest with St Johnstone's Steven Anderson and was under constant pressure whenever the ball entered his vicinity. The striker was getting nothing his own way and grew frustrated at being penalised by referee Iain Brines whenever he entered an aerial challenge with Anderson.
St Johnstone's defensive harrying was in tandem with their pressing game all over the field. Hearts were allowed little time on the ball even on their own 18-yard line as opponents scurried around to close down both ball and space. The visitors' only two chances of note in the opening period came in the final minute. First a turn and shot from Sam Parkin bounced around two yards wide of target before Collin Samuel headed weakly at MacDonald.
The second half began with another opportunity for McInnes' side. A free-kick hoisted to the back post found Dave Mackay with Novikovas having failed to track his man. Fortunately for the Lithuanian, Mackay's header flew across the face of goal and harmlessly out of play. Samuel then sprinted clear to collect Chris Millar's lofted through ball but his effort produced a straightforward stop from MacDonald.
Kyle limped off with a groin complaint to be replaced by Obua, and Ian Black then made way for David Templeton as Hearts shifted into a 4-4-2 formation. Within minutes they had carved open the opposition. Novikovas released Ruben Palazuelos down the left flank and he ventured forward to feed the ball to Stephen Elliott for a low left-footed cross. When the ball came in Obua seemingly only had to tap home from close range but somehow succeeded in clipping it over the crossbar.
As the game entered its latter stages St Johnstone's confidence grew visibly. Substitute Steven May came close after intercepting a poor header from Adrian Mrowiec, a moment which began a spell of concerted pressure by those from Perth. Eventually, it resulted in a priceless winning goal from MacDonald. "It just hit my shin and rolled past Bouzid and thankfully I managed to slot it away," he said.
Elliott had a late opportunity to equalise when Mrowiec's low ball into the penalty area broke for the Irishman, however his first-time shot was brilliantly parried by Peter Enckelman.
"I always felt there was a goal in us and when you've got somebody like Peter MacDonald on the bench, he's always liable to get one or two chances and thankfully he tucked one away. It came at the right time," explained McInnes.
"It was always a big ask to come here and get a result and I'm delighted we managed to get through to the next round.
"I still thought it was as decent atmosphere despite the one big stand being closed. We knew it was going to be tough but there was also a sense of excitement amongst our players because you could picture what it would be like at Tynecastle. That stand being shut didn't affect the game any. It was still an exciting tie and I think our supporters went home happy."