Rangers came from behind to beat Celtic 2-1 at home in a Scottish League Cup quarter-final on Wednesday, ending Celtic's run of seven consecutive wins in Old Firm matches.
The Scottish champions looked on course for an eighth victory in a row over their Glasgow rivals when John Hartson headed home in the 66th minute at Ibrox, but erratic play helped Rangers to mount a fightback.
Dado Prso equalised with five minutes left after Celtic had squandered possession before substitute Shota Arveladze fired the winner on the counter attack 10 minutes into extra-time.
It was the first victory by Rangers over Celtic since the League Cup final in March 2003, and their first at Ibrox since December 2002.
"I felt we showed some fantastic fighting spirit to come back," Rangers manager Alex McLeish told reporters. "The home fans spurred us on and we got some great commitment from the players.
"I thought we gave a good account of ourselves and we definitely deserved to edge it. With performances like that, we can now go on and win this competition."
Rangers, who have won the League Cup a record 23 times, dominated possession in the opening half as visiting goalkeeper David Marshall saved from Nacho Novo and Zurab Khizanishvili volleyed wide.
Celtic were fortunate to survive but an unmarked Hartson wasted the best chance of the half when he headed down and over from Alan Thompson's free-kick.
The visitors were unfortunate not to score when Stanislav Varga hit the bar on 64 minutes.
Two minutes later, Hartson put Celtic ahead with his header following a Thompson corner.
Prso levelled when Celtic lost possession, the Croatian striker scoring after Marshall failed to hold Hamed Namouchi's powerful drive on 85 minutes.
Rangers almost won it in the dying seconds when Agathe cleared the ball off the line from Jean-Alain Boumsong's header, but Arveladze settled matters in extra time when he rifled Fernando Ricksen's pass into the net.
Hearts claimed their place in the last four on Wednesday with a 3-1 win at Dunfermline Athletic.
Billy Mehmet's 60th-minute equaliser cancelled out Andy Webster's 33rd-minute opener, but Hearts went through courtesy of Paul Hartley's penalty on 66 minutes and a third from Joe Hamill six minutes from time.
They join Motherwell in Thursday's semi-final draw after their 5-0 drubbing of holders Livingston while Dundee United beat last season's losing finalists Hibernian 2-1 after extra-time in Tuesday's other quarter-final.