The Jambos led 2-0 after 30 minutes courtesy of goals from Darren Barr and Rudi Skacel, with Hibs skipper James McPake giving his side hope for the second half four minutes before the interval.
That hope was wiped out in four short minutes, as a second yellow card for Siakou Kujabi led to Daniel Grainger restoring the two-goal cushion from the penalty spot 90 seconds before Ryan McGowan headed home a fourth.
Skacel's second of the game 15 minutes from time was the icing on the cake as Hearts' three-year dominance over their neighbours moved onto a higher stage and brought home the silverware for Paulo Sergio's men.
Hearts dominated the opening half an hour, but took the lead in scrappy fashion after 14 minutes.
The first corner of the contest sparked a goalmouth scramble as the Hibs back line struggled to get the ball clear, allowing McGowan to have a second crack at goal after missing completely at the first attempt, and Barr was on hand to prod his effort beyond Mark Brown in goal.
Hibs continued to struggle for momentum as wide men Andrew Driver and Santana had their way on the flanks, and in the 27th minute an astute Ian Black ball into the area picked out Skacel, whose shot was deflected by McPake beyond Brown and in to double the advantage.
The second goal finally appeared to wake Hibernian up and a driven low centre from Kujabi was dummied by Isaiah Osbourne into the path of Garry O’Connor, who somehow blasted over the bar from 10 yards.
Driver produced more good work on 35 before floating in a cross which Suso Santana took a touch to control, allowing McPake to hurl himself in the way of the goal-bound shot.
But with four minutes remaining in the period, Hibs’ improvement over the previous 10 minutes paid off as Tom Soares’s low cross from the right was prodded over the line by McPake to give his side some hope.
The break for half-time would effectively signal the end of the men in green’s chances, however, as Santana dazzled his way towards the Hibs area only to be pulled back by the shirt by Kujabi.
The Gambian, already booked, received his marching orders for the foul but replays showed the offence came outside the box.
Nonetheless, Grainger buried the spot kick and Pat Fenlon’s side remained aghast at the turn of events less than two minutes later as three became four.
Skacel hooked a close range volley towards goal, forcing a great point-blank block from Brown, only for McGowan to follow up with a diving header to complete the capitulation.
Hearts unsurprisingly spent large spells spraying the ball around their own half for the remainder of the contest, as Hibernian fans headed for the exits with over half an hour remaining.
And Skacel, the only member of the side remaining from their last cup success in 2006, found the bottom corner with a scuffed rolling shot on 75 minutes to complete the rout.
Adding further misery for the green half of Edinburgh was Fenlon’s dismissal to the stands in the dying moments, as the ultimate dream scenario unfolded for thousands of jubilant Hearts supporters.