Manager Walter Smith fielded an unchanged team from Wednesday at a packed Caledonian Stadium with a record attendance of 7,753 present and Caley Thistle going into today's game on the back of five consecutive home wins.
On a bitterly cold day the game took a long time to warm up - the home side creating the first chance of the day in 24 minutes when Richard Hastings' cross found Markus Paatelainen in the clear only for his first touch to let him down, enabling Allan McGregor to block his effort.
Sixty seconds later a timely intervention from Carlos Cuellar denied Don Cowie as he moved onto a Ross Tokely cross.
These two near-misses appeared to wake the Light Blues up - Daniel Cousin's header from Chris Burke's cross being held by home goalkeeper Michael Fraser in 27 minutes.
The remainder of the first-half was turgid, sadly devoid of goalmouth incidents until the 42nd minute when Steven Whittaker's angled drive from a Steven Naismith lay-off was beaten wide by Fraser.
It had nevertheless been a poor first-half, with the home side successfully nullifying the Rangers threat. Recognising the need for change, Walter Smith subsituted Darcheville for Naismith at the interval.
Seven minutes after the restart Marius Niculae's twenty-yard drive from Ian Black's lay-off was held by McGregor as Inverness broke out in search of the opening goal.
At the other end Darcheville almost broke the deadlock in 58 minutes when his chip from an Adam cross just cleared the crossbar.
Three minutes later Adam's twenty-yard volley direct from a long McGregor clearance flashed just over.
Caley Thistle were still threatening however - Niculae's 25-yard shot being fisted away by McGregor in 68 minutes.
The game's most controversial incident arrived three minutes later when McGregor's long kick-out again found Adam who cut in from the left before curling the ball low into the far corner of the net. It seemed a perfectly good goal, but was disallowed on the say-so of linesman Terry Brunton who flagged for offside against Cousin who had run across the line of vision of Michael Fraser. There was just one thing wrong - Cousin, regardless of whether or not he had interfered with play, was not in fact offside, being played on by Russell Duncan.
Three minutes later Nacho Novo replaced Cousin as the Ibrox men pressed for a winner.
Inverness were far from out of it however - Niculae being denied by McGregor in 77 minutes when his shot from a Barry Wilson cutback was held by the 'keeper.
Rangers still looked by far the likelier however - five minutes later Adam struck the crossbar with a twenty-yard right-foot shot.
Time was running out when finally the breakthrough came - Brahim Hemdani's chip in 88 minutes being helped on by Whittaker and falling to Darchville who kept his cool to stab the ball into the net.
It was surely the winner - yet the home side had one final chance when Ross Tokely sliced the ball wide from a Cowie pass in injury time.
The final whistle signalled an important win for Rangers, and afterwards a relieved Walter Smith summarised:
"This was an important three points. We were delighted by the late winner. We didn't do well in the first-half when we had long periods of possession without threatening, but picked ourselves up in the second. We need to keep winning, but there's a long way to go."
INVERNESS CALEDONIAN THISTLE Fraser; Tolely, Proctor, Munro, Hastings; McBain, Black, Cowie, Duncan, Paatelainen (Wilson 68); Niculae UNUSED SUBS Malkowski, Bayne, Wyness, Vigurs, Gillespie, Duff
RANGERS McGregor; Whittaker, Cuellar, Weir, Papac; Naismith (Darcheville 45), Ferguson, Hemdani, Adam, Burke; Cousin (Novo 74) UNUSED SUBS Smith, Broadfoot, Boyd, Lennon, McMillan
REFEREE Charlie Richmond