Wonderful early strikes from Ellis Simms and Stephen Kingsley sent Hearts into the Scottish Cup final as 10-man Hibernian fell short with a fiery fightback at Hampden.
Hearts made the perfect start but spent much of the remaining time anxiously fending off their Edinburgh rivals.
Chris Cadden replied within 72 seconds of Kingsley's strike, and a fantastic Craig Gordon save denied Ryan Porteous a leveller. But although Hibs kept pressing after Joe Newell's dismissal, they could not find parity.
These two have been going at it since 1895 but this was just their fourth meeting at the national stadium. Hearts have won them all.
Not only do they have a chance of cup glory on 21 May but, with Sunday's semi-finalists Celtic and Rangers already assured Champions League places, it guarantees a crack at the group stage of either the Europa League or Conference League for the Tynecastle side next term.
It also ensures that two of Dundee United, Ross County and Motherwell will qualify for the Conference League.
It's a long way from little over a year ago, when Hearts were a Championship side reeling from the embarrassment of a Scottish Cup defeat to Highland League outfit Brora Rangers.
Following a typically frantic opening, Hampden was lit up by two special goals inside five minutes, with Simms clattering a shot home from 20 yards and Kingsley curling in a precise strike from a little further out after a well-worked set piece.
The packed-out Hearts end was going wild, with fans dreaming of another Scottish Cup derby drubbing like the ones dished out in the 2006 semi and 2012 final.
There were a few empty sections at the other end of the ground and there looked to be more vacant seats as some headed for the exits only to be brought back by Cadden's goal, slammed in after great tenacity in the box from Lewis Stevenson.
Hearts, who lost Andy Halliday and Craig Halkett to injuries in a thunderous contest, had a great chance to restore their cushion, only for Liam Boyce to drill inches wide in first-half stoppage time.
Following on from last weekend's derby defeat at Tynecastle, which consigned Hibs to a bottom six finish in the Premiership, it was to be another disappointing day for a club that has reached this stage of both cup competitions for three seasons running with nothing to show for it other than a couple of sets of losers' medals.
Shaun Maloney has made an unconvincing start to his managerial career but there were encouraging signs as he choose a more experienced and robust side, who fought for every inch of turf and were denied an equaliser early in the second half when Gordon somehow got fingertips to a Porteous header, diverting it against a post.
Hibs' continued ferocity was to be their undoing on 64 minutes when Newell was shown a second yellow card for a foolish, lunging tackle, while substitute Josh Campbell was perhaps fortunate to avoid a straight red for a rash challenge soon after.
The depleted underdogs continued to push for a leveller but patched up Hearts held firm amid the broiling froth and fury, with Gordon pushing away a free-kick from Sylvester Jasper deep into eight minutes of added time.
Man of the match - Stephen Kingsley
Kingsley was one of three Hearts players forced to hobble off injured at Hampden, having scored a great goal and putting in a shift to repel determined opponentsWhat did we learn?
Hearts were nowhere near their best as aggressive Hibs knocked them off their stride but they produced two top-class finishes and then dug in to book their place in the final.
Mounting injuries will be a concern for head coach Robbie Neilson, who is already without Michael Smith, John Souttar and Beni Baningime, but he can focus on what has been a fantastic season, wrapping up third place on returning to the top flight, with a return visit to Hampden next month.
This was Hibs' last chance to rescue what has been a miserable campaign and, while there was much to admire about their spirit, cooler heads were required and there remains a significant disconnect between midfield and attack.
What did they say?
Hearts manager Robbie Neilson: "It was a tough game, credit to both sets of players, it was a real nailbiter until the end.
"We did well to get the second then we made an error to let them back in, but the players did well to hang in and we deserve to go through.
"Now it will be about reinvesting the money we're guaranteed with the European football today's result has guaranteed."
Hibernian head coach Shaun Maloney: "I'm incredibly proud but disappointed the performance didn't match the result. It's by far the best performance since I've been here.
"We have to get to a point where we're more clinical. What I need to instil over the next four or five games, months, seasons - whatever it may be - is a level of performance, desire and physicality that we showed today.
"We need to instil that culture again and make sure we never feel like this again, particularly next season."
Player of the match
GordonCraig Gordon
Heart of Midlothian
Squad number1Player nameGordon
Squad number20Player nameSimms
Squad number3Player nameKingsley
Squad number19Player nameHalkett
Squad number5Player nameHaring
Squad number14Player nameDevlin
Squad number18Player nameMcKay
Squad number17Player nameCochrane
Squad number16Player nameHalliday
Squad number8Player nameMcEneff
Squad number21Player nameSibbick
Squad number15Player nameMoore
Squad number10Player nameBoyce
Squad number12Player nameAtkinson
Hibernian
Squad number16Player nameStevenson
Squad number27Player nameCadden
Squad number80Player nameHenderson
Squad number5Player namePorteous
Squad number4Player nameHanlon
Squad number22Player nameDoyle-Hayes
Squad number2Player nameClarke
Squad number25Player nameScott
Squad number6Player nameMcGinn
Squad number1Player nameMacey
Squad number11Player nameNewell
Squad number34Player nameMelkersen
Squad number20Player nameJasper
Squad number14Player nameMueller
Squad number32Player nameCampbell
Line-ups
Hearts
Formation 3-4-2-1
1Gordon
21Sibbick19Halkett3Kingsley
12Atkinson5Haring16Halliday17Cochrane
10Boyce18McKay
20Simms
1GordonBooked at 90mins21Sibbick19HalkettSubstituted forMooreat 50'minutesBooked at 84mins3KingsleySubstituted forDevlinat 87'minutes12Atkinson5HaringBooked at 82mins16HallidaySubstituted forMcEneffat 39'minutes17CochraneBooked at 70mins10Boyce18McKay20SimmsSubstitutes
8McEneff9Woodburn11Mackay-Steven13Stewart14Devlin15Moore30GinnellyHibernian
Formation 3-1-4-2
1Macey
6McGinn5Porteous4Hanlon
16Stevenson
27Cadden22Doyle-Hayes11Newell2Clarke
80Henderson25Scott
1Macey6McGinnSubstituted forCampbellat 74'minutesBooked at 82mins5Porteous4HanlonBooked at 82mins16StevensonSubstituted forMelkersenat 74'minutes27Cadden22Doyle-Hayes11NewellBooked at 64mins2Clarke80HendersonSubstituted forMuellerat 90'minutes25ScottBooked at 48minsSubstituted forJasperat 90'minutesSubstitutes
3Doig14Mueller20Jasper21Dabrowski23Allan30Hauge31Mitchell32Campbell33Bushiri34Melkersen36DelferriereReferee:John BeatonAttendance:37,783Live Text
Match ends, Heart of Midlothian 2, Hibernian 1.
Second Half ends, Heart of Midlothian 2, Hibernian 1.
Taylor Moore (Heart of Midlothian) wins a free kick in the attacking half.
Foul by Ryan Porteous (Hibernian).
Attempt saved. Sylvester Jasper (Hibernian) right footed shot from outside the box is saved in the bottom right corner.
Foul by Taylor Moore (Heart of Midlothian).
Ryan Porteous (Hibernian) wins a free kick in the attacking half.
Foul by Ellis Simms (Heart of Midlothian).
Jake Doyle-Hayes (Hibernian) wins a free kick on the right wing.
Cameron Devlin (Heart of Midlothian) wins a free kick on the left wing.
Foul by Jake Doyle-Hayes (Hibernian).
Craig Gordon (Heart of Midlothian) is shown the yellow card.
Toby Sibbick (Heart of Midlothian) wins a free kick in the attacking half.
Foul by Elias Hoff Melkersen (Hibernian).
Foul by Cameron Devlin (Heart of Midlothian).
Sylvester Jasper (Hibernian) wins a free kick in the defensive half.
Substitution, Hibernian. Sylvester Jasper replaces James Scott.
Substitution, Hibernian. Chris Mueller replaces Ewan Henderson.
Attempt missed. Elias Hoff Melkersen (Hibernian) header from the right side of the six yard box is close, but misses to the right.
Substitution, Heart of Midlothian. Cameron Devlin replaces Stephen Kingsley because of an injury.