The fact that Hearts can afford to leave two Scottish internationals on the bench is a testament to the fine job Jefferies has done since returning to the club he played for as manager at the start of the season.
He and Aberdeen's Roy Aitken have turned round the fortunes of their clubs who both flirted with relegation last year, and while Aberdeen have now failed to make their second final of the season and a possible Cup double, Hearts will make their first appearance in the Scottish Cup final for 10 years.
Both sides have been on the receiving end of five-goal beatings in recent weeks, but it was their midfields rather than defences which failed to deliver at Hampden. Aberdeen's Stephen Glass had come in from the left wing and struggled to impose himself in his new centre midfield role while Hearts' Steve Fulton was never given space as he was constantly choked by Paul Bernard.
It was after 80 minutes of tedious scrapping and misguided passes that Jefferies' substitutes combined to prompt an incredible final 10 minutes. McPherson nodded down to Robertson and while Aberdeen's defence managed to scramble his header away, the ball had clearly crossed the line.
Not to be outdone, Aberdeen's own substitute Duncan Shearer replied with three minutes remaining as his back-post header followed an arc across the front of goal and reached the inside of the side netting.
But the final decisive act came a minute into injury time when John Robertson crossed for the on-rushing Allan Johnston to direct a diving header through Michael Watt's fumbling fingers.
It seems the prospect of a Scottish Cup final can amplify even the quietest of men and it is clear Jefferies is looking forward to the 18 May. "Leading Hearts out on Cup Final day will be the greatest day of my life," he said.
Goals: Robertson (80) 0-1; Shearer (87) 1-1; Johnston 90 (1-2).
Aberdeen (4-4-2): Watt; McKimmie, Inglis, Smith, Woodthorpe; Miller (Grant, 54), Bernard, Glass, Robertson (Shearer, 71); Dodds, Windass. Substitute not used: Stillie (gk).
Hearts (3-5-2): Rousset; McManus, Bruno, Ritchie; Locke, Johnston, Mackay, Fulton (McPherson, 74), Pointon; Colquhoun, Lawrence (Robertson, 74). Substitute not used: Thomas.
Referee: W Young (Clarkston).
Bookings: Hearts: Mackay, Colquhoun, Johnston.
Man of the Match: Bruno.