Stevie Naismith’s winner ensured that Rangers ground out a victory over Motherwell to set up a Co-operative Insurance Cup final against Celtic.
Maurice Edu gave holders Rangers the lead after 20 minutes with a stunning long-range strike into the top corner.
Keith Lasley fired in a low drive from 18 yards for Motherwell’s deserved equaliser after 66 minutes.
But Nikica Jelavic set up Naismith to head Rangers’ second from 10 yards with 15 minutes remaining.
And the victory, which stretched the Ibrox side’s unbeaten run against Motherwell to 32 games since 2002, set up an Old Firm derby on Sunday 20 March.
Both managers had gone into the game by opting for experience in their starting line-ups.
Lasley was back in the Motherwell midfield in place of recent signing Steve Jones, while Rangers preferred Edu and Kyle Lafferty to Vladimir Weiss and Jamie Ness.
Steven Naismith celebrates his winner
Naismith scored the winner for Rangers at Hampden
Neil Alexander – replacing Allan McGregor in Rangers’ goal, as is now traditional for cup ties – was given an early touch with a Jamie Murphy drive that he handled with ease.
But Rangers dominated the early possession and Steven Davis slipped the ball into the path of Nikica Jelavic, but goalkeeper Darren Randolph raced off his line to gather before the striker could connect.
Edu weaved his way into the penalty box, Jelavic laid the ball into the path of McCulloch and the former Motherwell midfielder should have found the target with his drive from the edge of the penalty area.
A fierce Steven Whittaker free-kick from 20 yards was heading for goal before being diverted over the crossbar by a Motherwell shoulder.
The breakthrough came when Edu weaved his way past a couple of challenges and hammered a left-foot shot into the top corner.
However, Motherwell were looking good in possession and were looking as dangerous as the Scottish champions.
Steven Hammell’s short corner was met by Tom Hateley, but the midfielder’s powerful effort sliced high and wide.
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Smith delighted to reach final
Hammell had a go himself with a free-kick 35 yards out, but the Hampden turf took the pace off the ball and it was easily smothered by Alexander at his left-hand post.
Motherwell continued to press for an equaliser and Murphy tried his luck with an ambitious drive from 25 yards that was always rising well above the crossbar.
Edu placed another low drive on target, this time saved by Randolph at his near post, before the two sides were able to gather their thoughts in the dressing-room at half-time.
Motherwell had half-hearted claims for a penalty waved away by Willie Collum early in the second half when Davie Weir had an arm wrapped around John Sutton while rising to head clear.
The Fir Park side took heart and forced a fine save from Alexander, the goalkeeper rising to parry clear single-handed a thunderbolt by Steve Jennings from a similar area from which Edu had scored.
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McCall proud of Motherwell players
That was a warning Rangers failed to heed and, when Davis lost possession, Sutton played it into the path of Lasley, who fired low into the far corner from 18 yards.
A McCulloch header from a John Fleck corner flew a couple of feet over from 10 yards and the substitute set up Davis for a drive that was screwed wide from 16 yards as Rangers responded.
Just when it looked like a shock was on the cards, a beautiful crossfield ball from Davis found Jelavic and the striker’s cross was headed in by the unmarked Naismith at the back post.
Only a superb, point-blank save from Alexander prevented the tie going into extra-time when Steven Saunders rose high at the back post to meet a Murphy cross and direct a header low against the goalkeeper’s knees.
Murphy himself squandered Motherwell’s last chance in stoppage time when he fired low straight at Alexander from 16 yards.
