Zaliukas goal.
There can be little dispute that fortune favoured the Gorgie side, for Hibs had the bulk of the pressure and the creative play - but as so often in the past the day was won by hard graft and determination from a side who provided the perfect answer to the host of critics who had savaged the Tynecastle club in recent times.
The Leith men may have lost - but the man of the match without doubt was midfielder Scott Brown, strongly linked with a summer move to Rangers, who covered every inch of the playing surface driving his team on
Huge gaps in the Hearts end were perhaps symptomatic of the troubles engulfing the Tynecastle men at present, but they almost had something to cheer inside six minutes when Andy Driver's snap-shot was parried by home goalkeeper Andrew McNeil.
Hibernian were soon enjoying the bulk of the pressure however - Scott Brown's fifteen-yard shot being beaten away by Craig Gordon in fourteen minutes following a Christophe Berra error, then three minutes later Chris Hogg's header from a Scott Brown corner was headed off the line by Bruno Aguiar.
The Jambo support must have made the short journey across the city more in hope than expectation - but they were certainly relishing the afternoon as they taunted the home fans with chants of '105-in-a-Row', a reference to the length of time that has elapsed since Hibernian last won the Scottish Cup.
For all the Hibs pressure it was Hearts who twice came close to opening the scoring as the interval approached - firstly in 41 minutes when, bizarrely, David Murphy's attempted clearance 25 yards out saw Andrew McNeil scrambling back to touch the ball over the bar, then two minutes later Christos Karipidis' lob from the same distance was held by the goalkeeper on the line.
It had been a less-than-impressive derby, and the second-half was much of the same, yet just when a goalless draw appeared inevitable it was Hearts who broke the deadlock in eighty minutes when McNeil failed to properly clear a Driver free-kick, the ball falling to Zaliukas who volleyed home from fifteen
yards.
Hibs came fighting back - six minutes later Guillaume Beuzelin's twenty-yard shot from a Scott Brown lay-off was inches wide.
Substitute Ivan Sproule came even closer in 88 minutes when his angled drive following a Zaliukas error was parried by Gordon - Karipidis affecting a clearance, then in injury time Scott Brown's overhead kick from a Murphy free-kick was safely held by Gordon.
At the final whistle the Tynecastle fans celebrated long and loudly - delaying the home side's display of the League Cup for fully 45 minutes.
Afterwards Hearts Assistant Coach Stephen Frail summarised:
"We contained Hibs early on, but we were beginning to settle for 0-0. We needed to restore pride after the Dundee United defeat. There was a fantastic team effort today- - this win will go a long way to helping the club."
A crestfallen Hibernian Manager John Collins reflected:
"This is a cruel business. You don't always get what you deserve. We controlled large parts of the game, but our final pass wasn't good enough. Hearts defended well and stopped the flow of the game."
HIBERNIAN McNeil; Whittaker, Jones, Hogg, Murphy; Zemmama (Sproule 59), Scott Brown, Beuzelin, Stevenson (Stewart 73); Fletcher (Sowunmi 88), Benjelloun
UNUSED SUBS Simon Brown, McCann, Martis, Chisholm
HEARTS Gordon; Karipidis, Zaliukas, Berra, Goncalves; Ivaskevicius, Brellier, Aguiar, Pilibaitis (Jonsson 65), Driver (Fyssas 87); Velicka (Pospisil 76)
UNUSED SUBS Banks, Armstrong, Mackie, Kelly
REFEREE Kenny Clark
Attendance 15,953