Both goalkeepers were in good form to keep the first half goalless.
Former Kilmarnock hero Kris Boyd was frustrated by the offside flag in the early stages, but he forced Alan Combe into the first eye-catching save when he launched himself to the left to palm the striker's powerful 18-yard shot past his upright.
Steven Whittaker was a constant threat to the Kilmarnock defence and he forced Combe into another smart save with a powerful shot in the 32nd minute.
Kilmarnock too had their moments, particularly when the returning Danny Invincibile showed great technique to fire a thigh-high volley in on goal, but Allan McGregor acrobatically saved.
The second half was only seven minutes old when the deadlock was broken - and it was the visitors who took the lead.
Darcheville, a half-time replacement for the injured Daniel Cousin, fed the breaking DaMarcus Beasley who wriggled between three defenders before coolly finishing high into the net.
Darcheville created another opening two minutes later but Combe was well placed to save his powerful shot.
Combe came to Killie's rescue again after 59 minutes when he brilliantly blocked another excellent Whittaker effort from the edge of the box.
The home fans were sent into rapture two minutes later with a breakaway equaliser.
The ball broke to Steven Naismith from a Rangers corner and he beat Alan Hutton and found Colin Nish, who fed the supporting Invincibile.
The Australian striker only had the keeper to beat and he controlled the bouncing ball well to score.
Barry Ferguson almost put Rangers back in front within a minute, but his spin-shot was blocked by the Killie defence.
Rangers were clearly desperate to maintain their 100 per cent record and a rare David Weir mistake almost saw them go behind.
His slip gave Gary Wales a clear run on goal, but he made a bad decision trying to chip McGregor and the chance was lost.
But Darcheville calmed the Ibrox nerves in the 76th minute with the vital goal.
The striker went down looking for a penalty, but in the confusion the home side failed to clear their lines and the ball broke back to the bulky Frenchman who slotted low past Combe.