The decisive moment arrived just five minutes into the contest when the forward dispatched confidently from the edge of the penalty area, with the away side, buoyed by a terrific defensive display, showing resilience and togetherness in abundance to limit the Edinburgh outfit to very few sightings of goal.
Two points almost slipped through the visitors' fingers when Hibs were awarded a spot-kick with five minutes when Connor Barron clipped Junior Hoilett, but Butland was equal to Jamie McGrath's effort to secure a priceless three points in dramatic fashion.
It was a first league away outing for the Head Coach as he named five changes to his side from Sunday’s victory over Kilmarnock, with Max Aarons, Connor Barron, Nasser Djiga, Mikey Moore and Youseff Chermiti coming into the starting lineup.
The visitors wasted precious little time in bring the away crowd, nestled into the nearside corner of Easter Road, to their feet as the deadlock was broken just minutes into proceedings.
Chris Cadden was guilty of ceding possession in a dangerous area as Chermiti stole in, finding Danilo on the edge of the penalty area and the Brazilian planted a delicious finish on his unfavoured left side into the bottom corner and out of Raphael Sallinger’s reach.
Hibs looked to respond immediately through a Jamie McGrath strike, but the midfielder’s effort was straight down the throat of Jack Butland.
It would have been entirely against the run of play as Rangers soon restored their groove when Connor Barron snapped into a challenge to steal possession, with the ball breaking invitingly to Mikey Moore who swivelled 20 yards from goal and forced the Hibs goalkeeper to claw his effort around for a corner.
Indeed, the home side appeared spooked by Rangers’ shape, lined up with Aarons and Jayden Meghoma as wing-backs, as the Röhl’s side cut them open once again when a neat passage of play found its way to Chermiti who turned smartly but dragged his effort wide of the target.
Prior to that Meghoma had stung the palms of Sallinger when a header was cleared only as far as the on-loan full-back, who had earlier prompted an early caution for Chris Cadden when he hauled the England youth international back after being beaten all ends up.
The Hibs full-back was soon replaced by Miguel Chaiwa as the noise from the away end ratcheted up in appreciation of a positive opening period.
Grant Hanley was next into referee John Beaton’s notebook for a foul on Chermiti and it indeed illustrated that Rangers were a yard sharper to everything.
The half-time interval brought a double substitution as James Tavernier and Djeidi Gassama replaced Meghoma, on a booking himself, and goalscorer Danilo.
Hibs came out the blocks quickly and immediately posed questions of the Gers backline with lofted passes into the direction of Kieran Bowie leading the line.
It did lend itself to space opening up on the break as a driving run from Moore, initiated inside his own half, saw the winger beat several Hibs challenges, but he couldn’t quite work the space to deliver menacingly across the face of goal.
Barron then glided in-behind the Hibs midfield line from a throw-in as space opened up for an effort from distance, but his thunderous strike cannoned back off Grant Hanley and Hibs survived to tell the tale.
Opportunities were at a premium for both sides as Röhl turned to Thelo Aasgaard for inspiration in search of a second of the evening.
It almost arrived 19 minutes from time when Tavernier lifted a delightful free-kick delivery into the penalty area where Gassama nodded back across into a dangerous area, although a combination of Nasser Djiga and Derek Cornelius couldn’t make the required contact.
Still, Hibs were struggling to pierce a hole in a dogged Gers backline, marshalled superbly by John Souttar with Barron and Nico Raskin screening in midfield.
A deep cross swept towards Tavernier at the far post was volleyed back across goal by the captain but straight into the arms of Sallinger.
Drama ensued five minutes from time when Barron, immense in midfield, was guilty of tripping Junior Hoilett inside the penalty area and Hibs were gifted an opportunity to level from the spot.
But as has been the case so often throughout his Gers career, Butland rose to the challenge to thwart McGrath, sprawling to his right to deny the midfielder's low effort.
It was the perfect conclusion to an impressive showing from a Rangers perspective as the three points will travel back across the M8 motorway ahead of Sunday's Premier Sports Cup semi-final.
RANGERS: Butland, Djiga, Souttar, Cornelius (Fernandez, 89), Aarons, Raskin, Barron, Meghoma (Tavernier, 45), Danilo (Gassama, 45), Moore (Aasgaard, 63), Chermiti (Miovski, 76)
Subs not used: Kelly, Rothwell, Diomande, Curtis
HIBERNIAN: Sallinger, Bushiri, Hanley, Iredale, C. Cadden (Chaiwa, 22), Mulligan, Barlaser (Hoilett, 63), N. Cadden, McGrath (Campbell, 88), Klidje (Boyle, 63), Bowie (Youan, 63)
Subs not used: Smith, Obita, Mitchell, Megwa