Philippe Clement's team, who narrowly defeated Aberdeen 1-0 in last December's final, have secured a highly-anticipated showdown against their fierce rivals Celtic at Hampden Park on Sunday, December 15th.
Rangers were already feeling the heat after a 2-1 defeat to Aberdeen in the Scottish Premiership last time out left them nine points behind both the second-placed Dons and leaders Celtic - and that cranked up when former Ger Andy Halliday put Motherwell in front against the run of play after 25 minutes.
Clement's half-time team talk appeared to do the trick, however, with Cyriel Dessers atoning for missing a sitter before the break with a smart finish after the ball was fed into him by Connor Barron.
They had further chances to win the game, but it was not until the 81st minute that Nedim Bajrami collected a sweeping ball from Vaclav Cerny and clipped a shot that beat goalkeeper Aston Oxborough with the help of a deflection.
TrendingSmoke engulfed the arena due to pyros and flare from both ends of the ground which led to a delayed kick-off - as was the case in Saturday's semi-final - but when referee Nick Walsh gave the go-ahead the Light Blues took control.
Dessers should have sent Bajrami racing clear on goal but his pass was poor and intercepted, moments before Cerny's drive was saved by Oxborough, who would have a solid game.
In the 12th minute, Jefte played in Dessers but he dragged an unconvincing shot from 16 yards past the far post.
The Steelmen scored with their first chance, Steve Seddon crossing from the left for Halliday arrive at the back post - while Jefte ran away from the danger - and stab the ball past keeper Jack Butland before refusing to celebrate against his old team.
A lengthy delay while the VAR checked for an offside earlier in the move ended with referee Walsh confirming the goal and more cheers from the Well supporters.
Rangers' response was a powerful 20-yard drive from midfielder Connor Barron which was pushed round the post by Oxborough but the corner came to nothing.
An anti-board banner was revealed by the Union Bears, Rangers' ultras-style fans group, and the boos soon followed.
Gers' problems increased when Tom Lawrence picked up a knee injury and was replaced by Mohamed Diomande and when his curling shot in the 41st minute was parried by Oxborough, Dessers somehow missed the target with the loose ball.
The keeper made another save from a John Souttar header just before the break, with the Rangers players heading up the tunnel with the boos of their fans ringing in their ears.
Dessers got them back onside soon after the restart, however, when he converted Barron's pass from six yards.
As Rangers increased the pressure, Jefte cracked the post with a left-footed drive from the edge of the box and then skipper James Tavernier lofted a Bajrami cut back over the bar from six yards.
Cerny had two attempts on goal thwarted by the increasingly busy Oxborough and the Govan side kept pushing, with Motherwell's sporadic attacks still promising.
However, nine minutes from time, the Light Blues broke with pace and Cerny turned inside and set up Bajrami, whose shot from a tight angle clipped defender Kofi Balmer and sped past Oxborough, this time helpless.
Cerny struck the post in added time before Barron headed over but Well looked beaten.
Celtic, however, will prove an altogether different challenge in the final.