But, while their focus is now firmly fixed on Hampden and finding a way to overcome their last-four rivals and move beyond the semi-final stage of a major cup competition for the first time in three attempts this season, they know that they will have to deal with some unfinished business when they return to league duty on May 12.
That is when they will travel up to Pittodrie to face their third-place challengers.
They will do so with a slim three-point cushion, knowing that failure to win would see the season-long tussle continue into a tense final day of the season.
It was a source of frustration for everyone at Hibs that the match against St Johnstone did not leave them in an even better situation, especially as there was so little between the Leith side and their Perth counterparts.
But an uncharacteristic error from last weekend’s spot-kick hero Ryan Porteous, with just 22 minutes gone, handed the visitors an advantage and it was one they never really looked like relinquishing such was the paucity of goalmouth action.
Having done well to deal with the initial threat posed by Michael O’Halloran, Porteous attempted to clear his area with a pass straight to Glenn Middleton, who was placed perfectly, in a central position on the edge of the box, to send his effort into the net.
Shortly afterwards Hibs had the best chance to level. Drey Wright played a pass into Jackson Irvine and the Aussie swung in an inviting ball towards the back post. His international team-mate, Martin Boyle, stretched out a leg and managed to direct it goalwards with the outside of his right boot but, reading the danger, stand-in keeper Elliot Parish managed to stand tall and block.
The teams cancelled each other out in the remainder of the match, leaving Porteous in repentant mood as the team staged their post-match debrief.
“It happens. That’s the downside of being a defender, mistakes can be costly,” said Paul Hanlon of his young centre-back partner.
“He said he was just trying to clear it. I thought he had been trying to pick out a pass but he just mis-hit his clearance.
“It happens but he’s a good defender. When he makes mistakes, he reacts really well – and he did that. I’m more disappointed that we didn’t react well to going behind and didn’t manage to get back into it.”
That was hardly unsurprising given this season’s statistics. A more comfortable front-running side, they have only once fought back from a losing position to win a league match.
But, more comforting given their lead in the race for third is the fact they have not lost from a winning position.
“We’ve put ourselves in a position to go on and have a really successful season and we’re disappointed not to have sealed third place but our focus now shifts,” said Hanlon, who was part of the 2016 Scottish Cup winning team. "That’s the way it has to be for the next few weeks, fighting on both fronts. We’ve worked really hard to get in this position and we have to make the most of it.”