Second-half substitute Kris Boyd's late levellers (86 and 113) cancelled out Dundee United's earlier efforts from Noel Hunt (34) and Mark De Vries (96), to take the game to penalties where Rangers prevailed 3-2 after goalkeeper Allan McGregor denied David Robertson and Lee Wilkie.
The success is Rangers' 25th in the competition while Dundee United, fourth in the Scottish Premier League, last picked up silverware in 1994. Dundee United took a surprise lead eleven minutes before the break when Hunt scrambled the ball over the line at the far post, and it looked like Craig Levein's team would hold out until Boyd latched on to a weak back-pass from Mark Kerr with four minutes remaining.
Rangers fell behind again in extra time when a well-worked move from left to right ended with De Vries firing past McGregor from the edge of the area. However, Rangers broke Dundee United hearts for a second time through Boyd's header from Steven Davis' cross before McGregor's heroics in the shoot-out.
"I'm rather relieved as much as anything," said Rangers manager Walter Smith. "It was a very tight game and going to penalties is not good for the nerves. They've showed spirit throughout the season and worked very hard – they don't like to lose."
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