Morgan Cross' first-half strike proved decisive in the contest, and despite Rangers having the better of the opportunities - and playing the final half-hour with a player extra after Emma Lawton's red card - they were unable to muster a response.
Leanne Crichton named two changes to the side who were defeated by Glasgow City seven days ago, welcoming Mia McAulay and Kathy Hill back into the starting lineup.
These two sides last met in a Scottish Cup final back in 2023, with Celtic victors in a season where the Gers claimed the Sky Sports Cup.
However, the previous two editions of this trophy have belonged to Rangers, who were immediately on the front foot in a contest where nerves can be forgiven.
Indeed, it took until just after the 10th minute for the Gers to fashion their first attempt at goal, and they were certainly bemoaning their misfortune when it was the woodwork which denied them.
McAulay, introduced in place of Camille Lafaix in midfield, engineered the move when she tempted fellow Academy graduate Laura Berry down the right with a floated pass.
Berry did tremendously to hold the ball just long enough for McAulay to stride onto the return lay-off and rattle the outside of the post with a driven effort.
Without causing too many problems in attacking areas, Rangers were the better of the two teams in the opening blows.
The lively Berry was causing a few headaches with their purpose on the flanks, while 16-year-old May Cruft was as composed as ever in the engine room.
And yet Crichton’s side found themselves behind on 25 minutes when Celtic broke the deadlock.
Grant Scott’s side managed to keep the ball alive down by the nearside corner flag, and after Saoirse Noonan pinched possession and burst into space, a clipped delivery from the forward towards the far post was met on the full-stretch by Cross who slid home from close-range.
Rangers immediately sought a riposte as Eilidh Austin advanced down the right-hand side from full-back, aiming low across the face of goal with a delivery which was intercepted by Claire Walsh.
A neat Gers move on the left-hand side after McAulay robbed Noonan of possession on the halfway line almost fashioned an equaliser, with the 19-year-old striding onto another Berry lay-off after she received a pass from Calliste Brookshire and stinging the palms of Adelaide Gay in the Celtic goal.
Brookshire almost struck directly from a free-kick when she floated a dangerous delivery into the six-yard which Gay managed to claw to safety.
Moments later, the Greek international dovetailed effectively with Berry inside the danger area, whose clever lay-off was met by Austin first-time but the full-back watched her effort cannon off Chloe Craig.
If anyone in blue looked capable of levelling proceedings then it was certainly the effervescent McAulay, who suddenly found herself through on goal on the stroke of half-time after Wilkinson nodded into the teenager’s pass from a short goal kick. With only the goalkeeper to beat, however, the narrow angled and she shot straight into the vicinity of Gay.
The second period began sharply from Rangers as McAulay spun sharply and unleashed an effort at the Celtic goal which was comfortably gathered by Gay.
She was in the thick of it again just moments later, thwarting Berry after the Rangers forward was released down the right-hand side in a swift counter-attack.
Celtic were first to turn to their substitutes bench as Jennifer Smith replaced goalscorer Cross, and she was immediately involved in the action when she latched onto a loose pass and prompted a diving save from Jenna Fife down to her left.
Just 60 seconds later, however, Scott’s side found themselves down to ten players in a pivotal moment in the contest.
In truth, they could have no complaints as just minutes after full-back Emma Lawton went into the referee’s notebook for a cynical foul on Brookshire, she committed the exact same offence – on the same player no less – and was duly given her marching orders on the stroke of the hour-mark.
Celtic couldn’t get a handle on the Greek international as she continued to twist the defence inside out. Her low delivery moments later was spilled by Gay inside the six-yard box, but Berry couldn’t scramble the ball goalwards as it broke suddenly to the feet of the teenager.
Kim Shin Ji thought she had found the leveller with 19 minutes remaining on the clock, meeting Brogan Hay’s cross between the two Celtic central defenders but only looping her header onto the roof of the net.
A further change was made from Crichton when Lafaix replaced Cruft, signalling an intent to throw another attack-minded body forward in search of an equaliser.
Rangers came within inches - quite literally - of that leveller when an inswinging corner from Brookshire looked set to be heading straight over Gay before the Celtic goalkeeper desperately clawed the ball to safety via a ricochet off the underside of the crossbar.
Time was beginning to run out on the Gers, whose most likely avenue to goal appeared to be through Brookshire's wicked deliveries.
She soon received a short corner from Shin Ji as stoppage time approached, but her effort is wild as she let fly on Gay's goal.
There were cries for a penalty when McAulay went down under contact in the penalty area, but it was swiftly waved away as the referee soon blew the full-time whistle on the contest.
RANGERS: Fife, Austin (Hay, 64), Eddie, Hill, Docherty, Cruft (Lafaix, 75), Shin Ji, McAulay, Berry, Brookshire, Wilkinson
Subs not used: Kelly, Pegram, Sabajo, Mengwen, McLeary, Black, Boyce
CELTIC: Gay, Walsh, Robertson, Craig, Gallacher (Pritchard, 85), Rabjohn (Nakao, 73), Clark, Cross (Smith, 56), Luke (O’Hanlon, 73), Noonan (McGregor, 73), Lawton
Subs not used: Rodgers, Duncan, Dawson
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