As was the case in their last trip to Tynecastle, the Light Blues took until after the break to open the scoring and were even afforded the luxury of a missed penalty when Shota Arveladze saw his effort saved by the goalkeeper.
The margin of the victory hauled Rangers level with Celtic in terms of both points as well as goal difference, with the Light Blues assuming first place on the basis of having scored more goals.
Any doubts over Hearts’ commitment to this match – with their European place as good as already sealed – were answered throughout a torrid match in which they harried Rangers at every given chance allowing the Ibrox men no chance to rest on the ball.
Rangers seemed ill at ease trying to cope with this energetic approach from their opponents and, with their usual passing game disrupted, failed to create many clear-cut chances.
To add to their frustration, what fluid manoeuvres they could conjure up were regularly halted prematurely due to a figure in Light Blue – Michael Mols more often than not – wandering into an offside position.
Mikel Arteta struck the top of the crossbar with a cushioned drive after only three minutes but it was to prove something of a false dawn as goalkeeper Tepi Moilanen was rarely troubled again during the remained of the opening period.
As they proved with their recent win over Celtic, Hearts are a tough prospect to overcome at home and they posed a few questions of the Rangers defence throughout a stern 90 minutes.
The hulking figure of Mark de Vries was proving to be a real menace for Lorenzo Amoruso in an intriguing aerial battle while 18 year-old Graham Weir was simultaneously keeping Craig Moore occupied.
Hearts’ first attempt of a frantic first half came from the boot of Scott Severin whose powerful free kick was touched over by Stefan Klos before Barry Ferguson had a speculative effort deflected wide for a corner.
The Tynecastle side hadn’t managed a single goal against Rangers in four attempts this season but must have thought they were going to break their duck just before the break when de Vries slalomed across the penalty box only to see Klos brilliantly parry his shot on goal.
With anything less than a win inconceivable, Alex McLeish replaced the ineffective Arteta at half-time with Peter Lovenkrands to try to bolster Rangers’ lacklustre forward line.
It was Hearts though who opened the second half the stronger – de Vries forcing a solid save from Klos – before Neil Macfarlane and Michael Mols both earned bookings for an untidy squabble.
The match sprung once more into life shortly after the hour mark when Rangers were awarded a penalty when de Vries handled Fernando Ricksen’s corner right in front of ref Hugh Dallas.
After his double miss at Dundee, Ferguson passed the responsibility to Arveladze but the Georgian was to fare no better than his captain as his weak side-footed attempt was well blocked by Moilanen.
Arveladze’s redemption was to come just two minutes later when Rangers belatedly went in front.
Stephen Hughes slid a ball through to the former Ajax frontman and his cross was met at the near post by de Boer who powered a header into the roof of the net.
The elation – and relief – among the massive away support in front of Moilanen was almost tangible and they had further good news for them after 72 minutes when Rangers went further in front.
A long ball from Klos was nodded on by Amoruso into the path of de Boer whose cut back was gleefully slammed into the net by the on-rushing Lovenkrands.
With Hearts’ resistance seemingly finally broken, the Light Blues poured forward in search of further goals and Arveladze shot tamely at the goalkeeper after sub Steven Thompson had put him clean in on goal.
The home side came close to narrowing the deficit with just seven minutes after Amoruso mis-judged a threaded ball allowing de Vries a sight but Klos was alert to the danger and saved well from the Dutchman.
No further strikes followed for either side but Rangers will be satisfied with leaving Tynecastle with all three points that puts them in pole position in the title chase.
HEARTS: (4-4-2): 22 Moilanen; 17 Neilson, 4 Pressley (Simmons 75), 14 Webster, 2 Maybury; 12 Boyack, 21 Macfarlane, 6 Severin, 11 Valois (Kirk 77); 39 Weir (McKenna 64), 9 de Vries
Subs not used: McKenzie, Mahe
Booked: Macfarlane (52)
RANGERS (4-3-3): 1 Klos; 2 Ricksen, 3 Moore, 4 Amoruso, 5 Numan; 23 Arteta (Lovenkrands 46), 6 Ferguson, 27 Hughes; 14 de Boer, 10 Mols (Thompson 63), 24 Arveladze
Subs not used: McGregor, Malcolm, Caniggia
Booked: Mols (52), Amoruso (54)
Man of the Match: Craig Moore