Caniggia header puts Gers through
Substitute striker Claudio Caniggia scored with eleven minutes to go with a fine near-post downward header from man-of-the-match Mikel Arteta's free-kick.
The away side go away with the spoils after an exciting and open quarter final cup tie at East End Park, which saw The Gers have the better chances in the first half.
Dutch striker Michael Mols forced a good save from Pars goalkeeper Marco Ruitenbeek with his legs in the opening period.
Catalan midfielder Arteta then created the best chance of the half with a fine curling shot that Ruitenbeek made a superb diving save to keep it scoreless at the break.
Dunfermline's Stevie Crawford was a handful for the Ibrox club's defenders in the first half, as he kept them and Rangers goalkeeper Stefan Klos on their toes.
The second half saw a good spell of pressure from Jimmy Calderwood's side, with Barry Nicholson and Craig Brewster testing the Rangers net with half chances.
However, Rangers had quality going forward themselves and Barry Ferguson went close to giving his side the lead after latching on to an excellent passing move in The Pars' penalty box but his weak effort was stopped by Ruitenbeek.
The open style of play saw Dunfermline go very close to opening the scoring as a Nicholson shot agonisingly went off the legs of Brewster on the Rangers goal-line.
Moments later, a blistering Crawford strike from just outside the Rangers box forced Klos to make a great diving save to keep it 0-0.
The Pars were then denied a legitimate penalty claim when a cross from the left aimed for Nicholson saw Arthur Numan impede him from reaching the ball but the match referee waived off the home side's penalty claims.
It seemed the best opportunities for Dunfermline had gone when Rangers took advantage of a free-kick on the right of The Pars' box.
Arteta' fine ball into the box found the head of the Argentine Caniggia and his header was too powerful for Ruitenbeek to keep out.
With the win, Rangers move to the semi-finals of the Scottish League Cup, where they will play the winner of the Aberdeen versus Hearts quarter final in the first week in February next year.
Celtic have been drawn as the home side in their semi-final, where they will face the winner of the Livingston versus Dundee United quarter final.
Both CIS Insurance Cup semi-finals will be played at neutral venues yet to be determined.
CIS Insurance Cup - semi-final draw
Celtic - Livingston/Dundee United
Aberdeen/Hearts - Rangers
CIS Insurance Cup quarter final
Dunfermline Athletic 0-1 Rangers
