It was Nedim Bajrami who provided the crucial moment with ten minutes remaining, with the Albanian adding to Cyriel Dessers’ leveller shortly into the second period.
Indeed, the Gers were forced to take the scenic route after Andy Halliday opened the scoring midway through the first half, but a much improved second 45 minutes stretched the side’s winning run in the competition.
Philippe Clement’s side will return to Mount Florida next month to face Celtic in the final as they look to retain their grip on the trophy.
From the midweek match against Aberdeen, the manager made two changes to his side as Cerny returned from injury, with Jefte also coming back into the starting XI.
Rangers were first to threaten the Motherwell goal inside four minutes when Cerny collected a pass on the right-hand side and fizzed an effort on target which Aston Oxborough was equal to.
The Gers were certainly asking questions of the Steelmen’s backline, with Cyriel Dessers dragging a left-footed effort inches wide after he was released beyond the Motherwell defence.
A sweeping move from Clement’s side involving Cerny and Bajrami almost engineered an opener, with the latter laying a pass into the stride of Jefte who ballooned an effort over from the edge of the penalty area.
However, for all of Rangers’ early endeavour it was the Lanarkshire side who broke the deadlock from a familiar name.
Steve Seddon didn’t appear to have many Motherwell options inside the penalty area when the full-back picked up possession on the left-hand side, yet his curling delivery was met by Halliday making a run from deep and the former Gers midfielder stabbed the ball beyond Jack Butland at full stretch.
It meant Rangers had it all to do in their quest to defend their League Cup crown, with Connor Barron immediately setting about hauling the Light Blues back level when his rasping effort from 25 yards out forced Oxborough to tip the ball around for a corner.
Clement was forced to turn to his substitutes bench earlier than he would have hoped when Tom Lawrence was forced off through injury and replaced by Mohamed Diomande.
Indeed, the Ivorian almost restored parity on the stroke of half-time when his curling effort had Oxborough at full stretch and Dessers, haring in at the far post, contrived to push his rebound inches wide of the target.
Whatever message that was conveyed by Clement and his coaching staff at the half-time interval immediately paid off as the Gers levelled proceedings less than five minutes into the second period.
And it was a move of supreme quality which cut Motherwell apart, with Barron latching onto a pinpoint slide rule pass from Cerny before pulling the ball across to Cerny whose first-time finish was deft beyond Oxborough.
Rangers certainly had their tails up as a result of the equaliser and they almost celebrated an immediate turnaround when Jefte crashed a sumptuous half-volley off the outside of the post after the ball fell invitingly to the Brazilian on the edge of the penalty area.
Opportunity then knocked for James Tavernier shortly after when Bajrami made a clever darting run to the byline and picked out the captain at the far post, but the 33-year-old could not steer his finish on target with the ball arriving quickly.
Rangers’ most likely avenue to a second goal looked set to arrive from the dangerous Cerny, who combined neatly with Danilo and drew a smart stop from Oxborough down to his right.
From the resulting cross, meanwhile, the Czech winger arrowed a sweet volley which, again, was thwarted by the Motherwell goalkeeper.
It was little surprise, then, that it was the 27-year-old who was at the heart of the moment which completed the turnaround with ten minutes to play.
The Light Blues moved quickly to release Cerny on the right-hand side, allowing the winger to lift his head and pick out Bajrami bursting a gut on the opposite end. When it arrived at the feet of the Albanian, he worked the ball onto his left side and his finish took a nick off Kofi Balmer and over Oxborough from a narrow angle.
Motherwell appeared dead on their feet as the contest whittled into the final stages, and the Rangers players took the acclaim of the supporters at full-time when referee Nick Walsh blew for full-time.
RANGERS: Butland, Tavernier (Sterling, 66), Souttar, Balogun (Kasanwirjo, 77), Jefte, Barron, Raskin, Lawrence (Diomande, 35), Cerny, Bajrami, Dessers (Danilo, 66)
Subs not used: Kelly, Propper, Dowell, Igamane, Hagi
MOTHERWELL: Oxborough, Seddon (Sparrow, 55), Gordon, Balmer, Halliday, Stamatelopoulos (Tavares, 62), Casey, Kaleta (Blaney, 74), Wilson, Miller, Maswanhise (Robinson, 62)
Subs not used: Hegyi, Zdravkovski, Koutroumbis, Ebiye, Watt