The triumph, if one can call it that, was a far from impressive one, for Second Division Gretna could quite easily have created one of the greatest Scottish Cup shocks of all time.
Herats have ambitions of playing in the UEFA Champions' League next season, but quite frankly on this form they will be ripped to shreds by the first decent European side they are drawn against.
If there is one good thing to come out of today's result, it is that Rangers will now go straight into the First Round Proper of next season's UEFA Cup in September.
Gretna travelled to Hampden as massive underdogs, the gap between the two clubs in terms of League position being the greatest in the history of the national competition since 1927.
The Tynecastle men made no fewer than nine changes from Ibrox - and were on the attack from the opening minutes with Deividas Cesnauskis hitting a post with an eighteen-yard shot in seven minutes.
Four minutes later Rudi Skacel saw his 25-yard drive held by Alan Main, a losing finalist in 1991.
It was all Hearts at this stage - immediately afterwards Edgaras Jankauskas tested Main from a Skacel pass that the goalkeeper parried.
It seemed only a matter of time before the deadlock was broken - Bruno Aguiar cutting inside in 21 minutes before seeing his 25-yard shot deflected wide.
Four minutes later however - just to prove there were two teams on the park - Craig Gordon had to be alert to touch over Gavin Skelton's twenty-yard wide-angled free-kick.
Roman Bednar found himself in space at the back post from a Paul Hartley free-kick only for Main to turn his header wide of the target on the half-hour.
Five minutes later, as Gretna began to settle, Ryan McGuffie's header from a Skelton corner landed on the roof of the net.
The opening goal duly arrived in 38 minutes - a long throw from Robbie Neilson, headed on by Jankauskas, was volleyed home at the far post by Skacel.
Informed opinion during the half-time interval seemed to be that the Cup was in the bag for Hearts with that crucial breakthrough - but the second-half would be a different story.
Three minutes after the restart Steve Tosh should have levelled matters when he burst clean through only to shoot wide.
Hearts were growing more and more anxious as they sought the second goal that would kill the game - and Cesnauskis almost provided it with an eighteen-yard shot that was held by Main in 62 minutes.
Three minutes later Bednar saw his chip from a Jankauskas pass just clear the crossbar.
Gretna were growing more and more of a threat however - and substitute David Graham should have equalised in 66 minutes when his solo run took him clean through the opposition defence and round Craig Gordon, only for Steven Pressley to save the day with a last-gasp tackle.
Two minutes later Kenny Deuchar headed over from a Skelton corner - but the equalising goal was delayed only until 74 minutes when Referee Dougie McDonald awarded Gretna a penalty after Cesnauskis had bundled over John O'Neil (another survivor from 1991).
Ryan McGuffie took the spot-kick, only to see Gordon parry his effort - but the Gretna forward was sharp enough to react quickest and net the rebound.
For the pedantic amongst us , it was a second consecutive missed penalty in successive years (Chris Sutton being the guilty party last year) - but the Cup was now there for the winning.
Hearts almost regained the lead instantaneously when Skacel was inches away from connecting with a Jankauskas cross, then two minutes later Hartley's volley from Takis Fyssas' cross was inches over.
Goal-hero McGuffie almost snatched the Cup in 83 minutes when he burst through on a Mark Birch pass, only for Gordon to deny him with a one-handed save.
The resultant Skelton corner should again have provided the winner - but Gretna captain Chris Innes miskicked wide.
Extra-time it was, for the first time since 1991 to general astonishment, and Skacel might have put his side back in the lead one minute in with a 25-yard free-kick that was defelected wide.
Sixty seconds later Jankauskas headed wide from substitute Saulius Mikoliunas' corner.
Skacel (in what will be his last game for the club) saw his low drive strike an upright from a Michal Pospisil lay-off in 95 minutes, then sixty seconds later Hartley's 22-yard drive was turned wide by Main.
Gretna were not yet out of it however - Deuchar heading over in 97 minutes.
The game boiled over with just five minutes of extra-time remaining - Skacel, clean through on Main, stumbled as he was challenged by the goalkeeper but staggered on only to be dispossessed. Hearts protested long and loudly for a penalty - but the referee said no, and Hartley was yellow-carded for dissent, a caution that would prove costly for in the dying seconds the midfielder tangled with Derek Townsley on the touchline, aiming a kick at the Gretna defender, and received a second yellow, and subsequent red - although the offence could easily have merited a straight red.
Penalties were the order of the day, for the first time since 1990, and it was the SPL club who emerged triumphant when Townsley and Skelton both failed to convert their kicks.
Afterwards Tynecastle Coach Valdas Ivanauskas reflected:
"The win was the main thing. It's been a long and difficult season. We had so many chances to score a second. We gave Gretna the utmost respect. Rudi Skacel should have had a penalty, but the referee was very good today."
Vanquished, but unbowed, Gretna Boss Rowan Alexander was philisophical in his summing-up:
"I am very proud. We were playing against top-class opposition. We showed Scottish Football what we can do. We were apprehensive at the start, but defended very well. It has been a fantastic experience. There is a progressive spirit at the club. We began to believe that it might be our day as the game unfolded. We win most weeks, and have a winning metality."
Hearts owner - the controversial Vladimir Romanov - proclaimed afterwards:
"The balance of power in Scottish Football has shifted."
HEARTS Gordon; Neilson, Pressley, Tall, Fyssas; Cesnauskis (Mikoliunas 85), Hartley, Aguiar (Brellier 71), Skacel; Jankauskis, Bednar (Pospisil 69)
UNUSED SUBS Banks, Berra
GRETNA Main; Birch, Nicholls (Graham 55); Tosh, Townsley, Innes; O'Neil, McGuffie, Deuchar (McQuilken 102), Grady, Skelton
UNUSED SUBS Henderson, Mathieson, Berkeley
REFEREE Dougie McDonald
Attendance 51,232