Postpublished at 13:30 British Summer Time 28 April
Spartans 0-1 Hearts
Becky Galbraith goes racing onto the end of a loose ball but Charlotte Parker-Smith manages to come out and claim before the Spartans attacker can get to it.
Hearts set up a first Women's Scottish Cup final appearance against Rangers next month after brushing aside Spartans.
Both sides were making their Hampden debut but it was Hearts who looked most at home in a comfortable afternoon for Eva Olid's side.
Kate Mooney poked the Jambos into a half-time lead from close range before substitute Kathleen McGovern headed in a second with her first touch of the ball.
Carly Girasoli ensured Hearts would reach their first domestic cup final with an added-time nod.
Spartans failed to test Charlotte Parker-Smith in goal but Jack Beesley's attention will quickly switch back to league matters and ensuring his side's top-flight status.
Given their pedigree as the fourth force in the women's game, their recent historic win against Rangers and their unbeaten record against Spartans this season, Hearts were heavy favourites to be finalists on 26 May.
While they did not trouble Alicia Yates too much in the first half, their dominance was clear and their eventual opener was well deserved.
Georgia Timms hobbled off after appearing to plant her foot in the turf in the second half, but she played a pivotal part in the first as she provided the pin-point cross for Mooney to flick a cute effort home from nearby.
Spartans struggled to break free from their own half and their troubles continued and ultimately worsened in the second half.
Thirty-nine seconds after she was introduced, McGovern powered in from Monica Forsyth's teasing cross. McGovern then pitched a cross to the back post for Girasoli to head home and confirm the commanding win.
Forsyth, though, can count herself unlucky not to be on the scoresheet, having forced Yates to tip an effort on to the woodwork before cracking the crossbar with another fine strike.
Hearts were simply too good for Spartans, Jack Beesley even admitted that himself.
Even when they weren't celebrating one of the three well-taken goals, they were just toying with their bottom-six opponents.
Ciara Grant and Monica Forsyth were tremendous in midfield, driving their team-mates forward and keeping the potentially threatening Hannah Jordan extremely quiet.
Hampden is a big old pitch, and it will feel even bigger when all you're doing is chasing the ball. There'll be a few early nights among the Spartans ranks tonight.
It was as straight-forward an afternoon as Hearts could've asked for.
They've now had their taste of the national stadium and got a feel for the surroundings. When they come back here next month to take on Rangers, they'll need to up their game a couple notches and ensure no one is too overawed by occasion.
Spartans head coach Jack Beesley: "I am disappointed but I’m not too proud to say the better team won. Hearts are fourth in the league for a reason and we’re not, we’re at the start of our journey they’re slightly further along.
"Hopefully when the players wake up tomorrow they’ll realise what an achievement it was. I’m really proud of everyone."
Hearts manager Eva Olid: "We knew we were trying to balance between the emotions and focusing on the match. In the first minutes we were maybe a little bit nervous but then everything was fine.
"To score just before half time was so important to give us confidence. In the second half we played without pressure and played how we wanted to play."
It's a swift turnaround for both, with a league game to come on Wednesday. Spartans travel to Motherwell for a 20:00 BST kick-off, while Hearts take on Rangers - who they'll meet in the final - 10 minutes later in Glasgow.