French striker Jean-Claude Darcheville had put the Scottish side ahead against the run of play in the 60th minute and in injury time substitute Steven Whittaker scored a brilliant second to clinch the historic victory.
Rangers have never reached this stage in the competition before but their success came at a price.
Captain Barry Ferguson will sit out the first leg of the semi final against Fiorentina after receiving his second yellow of the competition, for kicking the ball away near the end.
And Kevin Thomson will also miss out after he too picked up another caution for a late challenge.
But at the end of the match Rangers manager Walter Smith was in no mood for negative thoughts.
He said: “Obviously we’re delighted to be in the semi finals. We worked very hard and played really well right from the off.
“I always thought we looked as we could get that killer pass which could gives us a goal but we never quite got there.
“Thankfully eventually we did get one to get the goal and then it was a terrific run by Steven for the second goal.
“Jean-Claude was excellent again and he’s beginning to get to the level of fitness he’s been trying to reach all season. We knew if we played as we did do in terms of possession and get up close to him we could get him running in on goal.
“We nearly managed it on a few occasions and then we finally managed to get the breakthrough in the second half.”
After the first leg in Glasgow had finished goalless, Sporting Lisbon were favourites to make the last four of the competition.
In the 18th minute only the woodwork denied the Portuguese side the lead.
Argentinean midfielder Leandro Romagnoli flighted a free-kick into the box and Brazilian striker Liedson raced in front of Rangers defender Christian Dailly to send a header beyond goalkeeper Allan McGregor only to see the ball bounce back off the post.
There were few other opportunities at either end until the 42nd minute.
Sporting captain Joao Moutinho drove in on goal and unleashed a low right-foot shot from 20-yards, which skimmed across the surface and just past the post.
At the start of the second half Sporting Lisbon piled the pressure on the visitor’s, who were forced into some desperate defending to keep their hosts out.
Simon Vukcevic almost gave the home side the lead in the 53rd minute with a glancing header from 12-yards which beat McGregor but dropped inches past the goal.
Rangers were rarely able to advance past the halfway line at this stage but in the 60th minute they took the lead.
Full-back Kirk Broadfoot launched a long ball out of defence which lone striker Darcheville headed into the path of supporting midfielder Steven Davis, who was racing up the right-wing.
The Northern Ireland midfielder returned the ball back across the face of goal and Darcheville, who had continued his run, coolly side-footed home from six-yards.
Sporting now needed two goals to stay in the competition but although they had several chances to score it was Rangers who grabbed the second goal of the tie in injury time.
Whittaker, who had replaced Lee McCulloch in the 77th minute, won a tackle in the centre-circle and, with the Sporting defenders continually backing off, carried the ball all the way into the 18-yard box where he dispatched a right-foot shot into the corner of the net.