Manager Walter Smith made two changes from a week ago with Kyle Lafferty and Darcheville replacing Steve Davis and Kenny Miller.
The Dons started adventurously - but it was the Light Blues who had a strong penalty claim in nine minutes when Darcheville's cross was punched away by Andrew Considine only for Referee Craig Thomson incredibly to turn a blind eye.
Sickening chants were filling the air from the visiting supporters. "Nice One Simmie" and songs about the Ibrox Disaster polluted the atmosphere. One wonders exactly when the football authorities will take action against this vermin?
A classic Rangers break in 25 minutes might have produced the opening goal when Pedro Mendes released Lafferty down the left - the Ulsterman's square pass finding Boyd who scooped the ball over the bar.
Four minutes later Barry Ferguson headed just wide from a Darcheville cross.
The referee demonstrated appalling judgement when he stopped play with Rangers in attack for treatment on Derek Young - it was to no-one's surprise that the player recovered in no time at all. Equally it was no surprise when Aberdeen booted the ball the full length of the park upon resumption. So much for sportsmanship...
The visitors came close to snatching the lead in 44 minutes when Young's shot from a Sone Aluko cross produced a fine one-handed save from Allan McGregor.
Rangers nevertheless finished the half on top - Charlie Adam's free-kick being headed towards his own net by Lee Mair only for Jamie Langfield to touch the ball over.
The Ibrox men restarted with Lafferty and Adam switching wings very much on the offensive - and might have broken the deadlock inside the opening sixty seconds when Mendes found Boyd whose reverse pass let in Darcheville whose shot was blocked by Langfield.
Jean-Claude finally broke the deadlock in 51 minutes when he scrambled the ball home following an Adam inswinging corner that was touched on by both Kirk Broadfoot and Boyd.
Aberdeen refused to lie down however - after all it WAS Rangers they were playing - and Zander Diamond saw his header from a Young corner headed off the line by Mendes in 65 minutes.
The Light Blues took heed of that scare two minutes later when another Adam corner, dummied at the near post by Lafferty created chaos in the visitors defence - allowing Boyd to head home.
That was the last action for the striker - for he was immediately replaced by DaMarcus Beasley.
Craig Thomson shamefully again took no action when Lafferty was elbowed in the face by Diamond. It should have been a straight red card for the defender.
Charlie Adam twice came close with free-kicks in the later stages of the game - firstly in 78 minutes when his cross broke to Lafferty who should have done better than shoot straight at Langfield, then six minutes later a 25-yard free-kick was inches wide.
There was yet more controversy in 85 minutes when Pittodrie substitute Chris Maguire - who had not so long ago shamefully abused Rangers on his own web-site - kicked out at Boyd on the ground. Once again it was a clear ordering-off, but unbelievably yet again the referee took no action.
Nevertheless the game was won - and the capacity crowd relished the closing stages when Rangers toyed with their opponents.
Afterwards Walter Smith summed up:
"We had to work hard for the win. People tend to take it for granted that we will win at Ibrox. Aberdeen played well. "
RANGERS McGregor; Broadfoot, Weir, McCulloch, Whittaker; Lafferty, Mendes, Ferguson, Adam; Boyd (Beasley 67), Darcheville (Novo 76)
UNUSED SUBS Dailly, Alexander, Edu, Aaron, Kinniburgh
ABERDEEN Langfield; Mair (Foster 70), Considine, Diamond, Mulgrew; McDonald, Severin, Kerr, Young (Maguire 70); Miller, Aluko
UNUSED SUBS Stewart, Bateman, Hodgkiss, De Visscher, Paton
REFEREE Craig Thomson