Arveladze and Mikel Arteta both sparkled on their return from injury but overall it was a Rangers performance where the emphasis was more on graft than craft.
Hearts hadn’t scored in their previous eight meetings with Rangers but here they took only 11 minutes to break that duck.
Their goal was no more than the visitors had deserved at that stage as the Light Blues found themselves on the back foot right from the first whistle.
Despite the absence of three first-choice defenders through injury and suspension, Hearts surprisingly still chose to deploy Kevin McKenna as an auxiliary attacker.
The decision almost paid off after just six minutes when the towering Canadian’s snapshot was gratefully gathered by Stefan Klos and Rangers had another lucky escape moments later when Fernando Ricksen nodded Robert Sloan’s corner narrowly passed his own goal.
It seemed only a matter of time before Hearts finally found the target and perhaps unsurprisingly they finally struck gold from another of Sloan’s sweet inswinging centres.
After Ricksen’s near escape, McKenna saw a header cleared off the line by Arveladze before they made it third time lucky when Sloan’s corner fell to Andy Kirk at the back post and he stabbed in a low trundler that trickled over the goal line.
Rangers were struggling to gain any sort of foothold in the match although the inspirational Georgian came close with a free kick after Michael Mols had been dragged back by Patrick Kisnorbo.
Hugh Dallas chose not to book Kisnorbo on that occasion and there was further controversy later in the half when the referee chose not to penalise the Australian defender at all when he again seemed to impede Mols.
Had the whistler played to the letter of the law then Kisnorbo should have picked up his second yellow card for that incident after 42 minutes and Hearts should have been down to 10 men.
The Australian was eventually booked in the second half for dragging back Peter Lovenkrands as he strode purposefully towards goal.
By that point, Rangers had clawed their way back into the match and had managed to carve out an equaliser after 21 minutes.
It was a well-worked goal. Ricksen’s diagonal ball sent Mols through on goal and, when his shot was acrobatically blocked by goalkeeper Craig Gordon, Arveladze sprang highest to head the loose ball into the net.
Gordon, who recently took over from Tepi Molianen between the sticks, was impressive throughout the 90 minutes and twice denied Rangers as they sought to move in front.
He reacted instinctively to keep out Peter Lovenkrands’ close-range volley after 24 minutes before sticking out a fist to block Arveladze’s header as half-time approached.
It was by no means one-way traffic as play raged from end to end. In the 40th minute Neil Macfarlane’s cross slid right across the goal to the waiting Sloan whose powerful effort was well parried by Klos and a minute later Kirk headed another great chance just wide.
It had been a frantic opening 45 minutes and the second half was just as chaotic.
Another chance went a-begging for the unfortunate Mols just five minutes after the re-start when a brave block by Scott Severin cut out his net-bound effort but the Dutchman was to play a significant role when Rangers went in front just a minute later.
Latching onto a ball from Lovenkrands, Mols hared down the left touchline before playing in a perfectly-weighted centre that Chris Burke battered over the line from a matter of feet.
Burke had been well shackled up until then but, moments after his strike, he was allowed to tear down the right wing, skipped between two defenders before releasing Arveladze.
The Georgian timed his shot well but could only watch as it trickled agonisingly past the post.
Hearts again refused to buckle under the Rangers’ pressure and only a breath-taking fingertip save from Klos kept out another header from the towering McKenna who shook his fist at the sky in frustration like a cartoon villain.
The match finally slowed down to a more sedate pace amid a welter of substitutions from both sides.
One of those replacements, Egil Ostenstad, had a chance to make an immediate impact with just 11 minutes remaining but wastefully headed Lovenkrands’ cross high into the stands.
Hearts threw on Mark de Vries in a late bid to salvage something from the match but Rangers head on to claim the points, with Klos gratefully grabbing a last-ditch volley from Robbie Neilson to deny a late Hearts rally.
RANGERS (4-4-2): 1 Klos; 2 Ricksen, 12 Malcolm, 25 Berg, 18 Ball; 30 Burke, 27 Hughes (Ross 57), 23 Arteta, 26 Lovenkrands; 7 Arveladze, 10 Mols (Ostenstad 74)
Subs not used: McGregor, Capucho, Vanoli
Booked: Ball (40)
HEARTS (4-4-2): 13 Gordon; 16 Neilson, 20 Kisnorbo, 7 Severin, 3 McCann; 8 Stamp (de Vries 82), 18 Hartley, 14 Macfarlane, 23 Sloan (Weir 78); 10 Kirk, 5 McKenna
Subs not used: Moilanen, Simmons, Berra
Booked: Kisnorbo (65)
Man of the Match: Shota Arveladze