At a rocking Ibrox, the home side started with intent as captain James Tavernier opened the scoring early on to become the leading scorer in the competition this season with seven goals.
Glen Kamara added a second before the half-hour mark in a game dedicated to legendary Rangers kit man Jimmy Bell, who died earlier this week.
Christopher Nkunku then levelled the tie for Leipzig in the second half, but Lundstram smashed home the winner in the 80th minute.
Please use Chrome browser for a more accessible video player Former Rangers striker Kris Boyd describes his former side's 'unbelievable achievement' as they beat RB Leipzig to reach the Europa League final in Seville
Rangers face Eintracht Frankfurt - who beat West Ham 3-1 on aggregate - in the Europa League final in Seville on May 18, looking to go one better than in 2008 when they lost the UEFA Cup final to Zenit Saint Petersburg.
Spanish volunteers in Axis service\n\n Although Franco did not bring Spain into World War II on the side of the Axis, he permitted volunteers to join the German Army on the clear and guaranteed condition they would fight against Bolshevism (Soviet Communism) on the Eastern Front, and not against the western Allies.
One of the main reasons was that Spain was still recovering from its own civil war, which had ended in 1939, just before the outbreak of World War II. Additionally, Spain's dictator at the time, Francisco Franco, was wary of becoming directly involved in another major conflict so soon after the Spanish Civil War.