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.
Walter Smith's men have now played a staggering 16 games in Europe this season, as they remain in the hunt for four trophies, in what has been the veteran boss' best continental run since narrowly missing out on the Champions League final back in season 1992/93.
Luca Toni's last-minute header gave Bayern Munich a dramatic away-goals victory over brave 10-man Getafe and a place in the last four of the UEFA Cup.
Toni stuck twice in the last six minutes of extra-time to earn a 3-3 draw for the German outfit, who were heading out of the competition in normal time before Franck Ribery popped up in the last minute to cancel Cosmin Contra's opener.
A virtuoso performance by Adrian Mutu inspired Fiorentina past PSV Eindhoven.
Mutu struck at either side of half-time, his opener a stuning 30-yard strike, as the Italians dominated at the Philips Stadion to earn a 3-1 aggregate success and book a meeting with Rangers in the last four.
Zenit St Petersburg also progressed despite a 1-0 defeat to Bayer Leverkusen in Russia on Thursday night.
Dmitri Bulykin made the most of a rare start to score the only goal of the game but it was nowhere near enough to overturn Zenit's 4-1 advantage from the first leg.