Scorers: Rangers - Clark (44), Miller (63)
And, with the South Africa-based millionaire watching on from the Bill Struth Main Stand for the first time since a 1-1 draw with Queen of the South in early March just days after a shareholder vote swept him to power, the team did not let him down.
Clark’s tidy finish a minute before the interval after some Haris Vuckic brilliance was perfectly timed for the hosts as they overcame a nail-biting opening period. And Miller’s second after 66 minutes means the Glasgow giants are now the firm favourites to progress to a final showdown with Motherwell later this month.
While Hibs were sunning themselves in La Manga in preparation for this game, Rangers had been forced to graft for their semi-final slot.
Boss Stuart McCall named the same side which came through Sunday’s nervy quarter-final decider with Queen of the South.
When the teams last met in Edinburgh two months ago, McCall had opposite number Alan Stubbs fooled with a surprise 3-5-2 formation as he ended a run of three straight defeats to the capital city men.
This time, though, he stuck with the back four of Richard Foster, Darren McGregor, Marius Zaliukas and Lee Wallace, which creaked and groaned during that narrow 3-2 aggregate win over the Doonhamers.
Hibs - fully rested 18 days on from their final Championship game - meanwhile, made two changes to the team which beat Falkirk to pip Gers into second place, with David Gray and Fraser Fyvie starting at the expense of Jordan Foster and Martin Boyle.
The home fans among the 41,236-strong Ibrox crowd outnumbered the travelling support 40 to one as the atmosphere crackled before kick-off crackled, mostly with tense angst.
As expected both sides set about things at a 100mph pace, but goalmouth incidents were scarce. Two harmless efforts from visiting captain Liam Craig were the best either side could manage in the opening quarter-hour.
It took 22 minutes for Rangers to build some kind of sustained pressure, but Miller’s shot straight at Mark Oxley was the not the climax Rangers hoped for.
Hibs were more adventurous although Dominique Malonga failed to pick out Jason Cummings at close range when Zaliukas’ slip opened up space.
With the clock ticking towards half-time, Rangers were looking short of ideas in the final third - but Vuckic’s moment of inspiration a minute from the break was just what they needed.
Up against Craig and Lewis Stevenson, there looked nowhere to go until he scooped the ball over the Hibs duo for Foster to run onto and square for Clark, who finished from six yards out.
Oxley had to hold on to a Vuckic strike early in the second half as the Light Blues looked to consolidate their lead, but Malonga wasted a header from Scott Allan’s corner that should have found its way into Cammy Bell’s net.
The next goal was always going to be crucial and the home faithful roared with delight as it went their way. Dean Shiels pulled the trigger from 25 yards but, when his shot span up off Craig’s back, Gers did not stop. Stand-in skipper Wallace was up to nod it into the box, where Miller had stolen in unnoticed at the back post to prod under Oxley’s body.
The goal had Ibrox rocking but Malonga missed another chance to hush the jubilant home fans when he fired over from another Allan corner.
Hibs piled forward towards the end looking for something to take back to Easter Road but this time the Rangers defence refused to waver.
Foster then almost killed the tie off completely. but Oxley pushed his shot over in stoppage time.