Manager Walter Smith made two changes from last weekend with Madjid Bougherra and Nacho Novo replacing Steven Whittaker and Charlie Adam..
When Rangers last faced Caley Thistle they were five up by half-time, but there was never the slightest prospect of that happening today.
Novo almost produced a spectacular opener when, spying home goalkeeper Ryan Esson off his line, he produced a forty-yard lob that just cleared the crossbar.
Four minutes later a power cut affected the entire stadium, knocking out the floodlights - thankfully with a 12.30pm kick-off there was little prospect of the game being abandoned.
Sixty seconds later Inverness threatened when Roy McBain's cross found Andy Barrowman whose header was blocked by Allan McGregor, the loose ball being cleared off the line by Bougherra.
Don Cowie - linked recently with a move to Ibrox - was next to test McGregor in 24 minutes when his eighteen-yard shot was beaten out by the goalkeeper.
Rangers finally called home goalkeeper Ryan Esson into action on the half-hour mark when Kenny Miller broke through the heart of the Caley defence, the ball breaking to Steve Davis whose volley was held by Esson.
It was end-to-end action - six minutes later Ian Black's 25-yard effort from an Iain Vigurs pass was held by McGregor, then at the other end Boyd fired over from Miller's cross.
Vigurs cut in from the left in 41 minutes only to see his drive shave the side-net - then in the last action of the half Boyd's header from a Davis corner was held by Esson.
It had been a poor opening 45, but Rangers broke the deadlock 23 seconds after the restart with a classic strike from Pedro Mendes who curled a 25-yard shot home after Novo's low cross had been back-heeled into his path by Miller.
inverness were not finished yet however - Cowie's cross being headed just over by Barrowman in 52 minutes.
Six minutes later Novo's snap-shot from the edge of the area was held by Esson.
An unhappy Miller was replaced by Chris Burke in 61 minutes - the striker snatching a coat from Jimmy Bell and marching straight up the tunnel.
The substitute soon made an impact - within six minutes he made an opening for Boyd whose shot on the turn was blocked by Esson.
Caledonian full-back Ross Tokely almost scored a spectacular second for the visitors on seventy minutes when - following a Novo counter-attack - he volleyed a Mendes cross towards his own net only for Esson to produce a superb diving save.
Rangers were going all-out for a clinching second goal - within the next five minutes Burke's volley from a Barry Ferguson pass was just over, then Novo's shot on the turn from a Boyd knock-on was held by Esson.
There was an injury worry for the visitors in 77 minutes when Mendes was replaced by Whittaker - yet within sixty seconds Burke cut in from the left before sending a low eighteen- yarder inches wide.
A one-goal lead is never a secure one - as was illustrated all too clearly in 79 minutes when Barrowman's twenty-yard shot was beaten out by McGregor.
In an instant however the visitors had made the game safe with a second goal when Boyd shot home on the turn following a Kirk Broadfoot - Steve Davis move.
Six minutes later Boyd again found the net with a header from a Burke cross to make it 3-0.
Afterwards Walter Smith summarised:
"We were poor in the last thirty minutes of the first-half, but I made the players aware at the interval that we would have to raise our game. The second-half was much better - the first goal helped set the tone for what was to folliow."
INVERNESS CALEDONIAN THISTLE Esson; Tokely (Duff 83), Proctor, Vigurs (Rooney 72), Munro, Hastings; Cowie, Black (Imrie 63), McBain, Duncan; Barrowman
UNUSED SUBS Fraser, Djebi-Zadi, Sutherland, Wood
RANGERS McGregor; Broadfoot, Weir, Bougherra, Papac; Davis, Mendes (Whittaker 77), Ferguson, Novo; Boyd, Miller (Burke 61)
UNUSED SUBS Alexander, Lafferty, Aaron, Velicka, Fleck
REFEREE Dougie McDonald