The Tynecastle side have stuttered in the league this season but turned in a disciplined performance as Celtic missed out on a last four place in this tournament for the second year running.
Hearts started the match brightly, using the extra personnel in their five-man midfield to hold on to possession.
However, the hosts were first to threaten when Aiden McGeady embarked on a lung-bursting 70-yard run down down the left flank before firing across the face of goal and wide.
Celtic gradually upped the pace after a sluggish opening and McDonald drew a save from Basso with a shot from point-blank range.
McDonald was then slipped in by a great pass from the impressive McGeady and cut into the box from the left, only to chip over the crossbar.
The home side could have snatched the lead just before the break when Paul Hartley played a short free-kick to Scott Brown and the Scotland midfielder's dipping strike from distance had to be tipped away by Basso.
Brown and McDonald linked well early in the second period but the Australian striker's shot was saved smartly by the feet of Basso.
Close to the hour mark, Brown was again the creator, swinging in a dangerous cross that the stretching Sno could only divert over the top from inside the six yard box.
Hearts' lone striker Calum Elliot was not seeing much of the ball but did manage to send in a neat shot on the turn from 20 yards only to see it float straight into the arms of Artur Boruc.
With 69 minutes gone, Donati did well to dance past two Hearts challenges and his low strike from the edge of the penalty area was well held by the increasingly busy Basso.
Sno then blazed a great chance over the crossbar after more good set-up work from Brown.
And Celtic were made to pay for the profligacy when the visitors snatched a goal from a swift counter-attack.
Andrew Driver did well to keep the ball in play and, with several home players claiming a throw-in, ran out to cut the ball back for Velicka to pick his spot in the far corner of the net from 14 yards.
McGeady tested Basso with a fierce shot, with Chris Killen firing the loose ball too high from a tight angle as Celtic came roaring back.
However, Velicka stunned the home crowd further when he picked the ball up on the edge of penalty box and smashed a screamer beyond the despairing Boruc and into the top corner of the net.
Celtic: Boruc, Caldwell, Kennedy, McManus, Naylor (Sno 46), McGeady, Scott Brown, Donati, Hartley, McDonald, Vennegoor of Hesselink (Killen 72). Subs Not Used: Mark Brown, Jarosik, O'Brien.
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