Substitute Steven Whittaker then added a second deep into injury time to provide the perfect end to a memorable clash.
The 2-0 aggregate win means Rangers will appear in the last four of the competition for the first time when they face Fiorentina, who defeated PSV Eindhoven.
Sporting’s chances had been limited early on but they hit the woodwork when Leandro Romagnoli’s free-kick found Liedson and his header smacked off the post.
But Rangers hung on in there and when Darcheville (60) played the ball out to Steve Davis out on the right he raced into the box and collected the return pass before slipping the ball home.
And late on Whittaker applied a cool finish after a solo run from his own half.