Ronald de Boer missed a penalty with three minutes of extra-time remaining, but it was a spurned spot kick at the sudden-death stage by Paris St Germain defender Mauricio Pochettino that sent Rangers into the last 16 in a 4-3 penalty shootout.
Lorenzo Amoruso, Russell Latapy, Arthur Numan and Barry Ferguson were the successful penalty takers, with Bert Konterman and Claudio Caniggia both hitting the crossbar.
Stefan Klos saved Jay-Jay Okocha's first effort for the home side, and by the time Pochettino stepped up it was sudden death.
His shot hit the top of the crossbar and Rangers were the victors after 210 minutes of goal-less football at both Ibrox and the Parc des Princes.
PSG: Letizi, Heinze, Pochettino, El Karkouri, Cristobal, Ogbeche (Okocha 57), Cisse (Mendy 78), Arteta, Ronaldinho Gaucho, Aloisio, Leroy (Anelka 63). Subs Not Used: Alonzo, Potillon, Dias, Llacer. Booked: Cisse, Anelka, Mendy, Letizi.
RANGERS: Klos, Amoruso, Konterman, Moore, Ross (Vidmar 109), Reyna, Ferguson, Numan, de Boer, Flo (Latapy 78), Lovenkrands (Caniggia 31). Subs Not Used: Dodds, Mols, Wilson, Christiansen. Booked: Ross, Ferguson.
Referee: H Strampe (Germany).