Rangers made four changes to the side which drew against Dundee United on Sunday.
Christian Dailly moved to centre-half to cover for the suspended David Weir.
Darcheville was used in the lone striker role, and Kirk Broadfoot, Brahim Hemdani and Steven Davis were all restored to the starting line-up.
Sporting were without injured Brazilian centre-half Anderson Polga, with Gladstone replacing him for the Portuguese.
Darcheville spurned a great chance within three minutes when he collected Hemdani's pass, but delayed his shot and his effort was brilliantly blocked by Gladstone.
The Frenchman's movement was causing the home defence problems as Rangers searched for a vital away goal.
Sporting almost made Rangers pay for their profligacy after 18 minutes.
Whittaker danced through the Sporting defence to make it two
Leandro Romagnoli's free-kick was headed goalwards by Leidson, but the Brazilian's effort came back off the post and bounced to safety.
Rangers appeared content to concede possession to Sporting and throw a blue curtain around McGregor's goal.
Vukcevic and Miguel Veloso went close before the break but Rangers repelled every Sporting foray forward.
Sporting attacked Rangers with greater intensity at the start of the second-half.
Vukcevic's glancing header evaded McGregor's despairing dive but slid wide of the post.
Darcheville, a thorn in Sporting's side throughout the match, gave Rangers the lead with half an hour remaining.
Sporting failed to clear Kirk Broadfoot's long ball and Darcheville headed the ball wide to Davis.
The Northern Irishman's cross was superbly driven home by Darcheville to send the visiting fans wild.
Cousin replaced the tiring Darcheville with 19 minutes remaining, as Sporting's attacks became increasingly desperate.
Joao Moutinho stung McGregor's palms with a fierce shot from the edge box as the home fans urged an equaliser.
Cousin could have doubled Rangers lead late-on, before Whittaker danced through the Sporting defence to score a superb individual goal and cap a memorable night in Lisbon.
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