In a dominant display from start to finish, the scoring was initiated by Laura Berry before a rampant first half was capped off by a Demi-Lee Falconer own goal and a cultured Eilidh Austin finish.
Chances beckoned for the Gers in the second period, but an inspired display from Thistle goalkeeper Jennifer Currie between the posts halted the scoring as Academy players Saoirse Coyle-Morrow and Erin O’Brien celebrated their senior debuts off the bench.
The draw for the last four will take place on Tuesday afternoon as Rangers seek a fourth successive triumph in the competition.
Crichton named two changes to her side from last weekend as Jess Pegram and Camille Lafaix came into the starting lineup.
On the substitutes bench, meanwhile, sat the Academy trio of Erin O’Brien, Phoebe O’Donnell and Saoirse Coyle-Morrow.
The opening stanza was interrupted by a lengthy injury stoppage as Hannah Robinson was stretchered off for the visitors after going down in significant pain midway inside the Rangers half.
Our best wishes go to the Thistle midfielder who was replaced by Mae English inside a quarter of an hour.
Back to the action and Mia McAulay dragged wide just minutes later, before Berry turned provider on the right-hand side for Katie Wilkinson who contrived to shoot wide first-time with the goal gaping.
However, the hosts didn’t have to wait too long to break the deadlock and it was one Academy graduate to the other as Jodi McLeary combined expertly with Berry before the latter swivelled smartly inside the penalty area and slammed an unerring finish in off the underside of the crossbar.
Rangers were certainly in the mood with a place in the last four at stake, with Quinty Sabajo working a dangerous shooting opportunity which was pushed away by goalkeeper Currie and lifted over on the rebound by Eilidh Austin.
The aforementioned Austin was the architect just beyond the midway point of the first half as the Gers doubled their advantage in Cumbernauld.
Having been released down the right-hand side, she centred smartly in search of Wilkinson but the delivery was turned into the Thistle net by one of their own before it reached the forward as captain Demi-Lee Falconer was the guilty party.
It was one-way traffic at Broadwood as Lafaix was next to go close when she worked a shooting chance on her favoured right side and prompted a smart diving stop from Currie.
The half-time whistle couldn’t come quickly enough for the away side, but they were picking the ball out of the back of the net for a third time seven minutes prior to the interval.
Austin was proving a thorn in the Thistle side down the right-hand side and it was only fitting that she wrote her name into the scoresheet when she exchanged passes with Berry and stroked a delicious finish into the far corner which left Currie stranded.
The hosts almost celebrated a rare goal from the captain when Docherty let rip from 20 yards out and forced the Thistle goalkeeper to tip over the crossbar at full stretch. From the subsequent corner, Berry was the beneficiary of a short corner routine and lashed wide of the target.
Wilkinson very seldom goes into the second half of a game without a goal to her name and she very nearly corrected twice in quick succession when her dipping free-kick floated wide before she rattled the woodwork with a thunderous effort from distance.
A swift breakaway on the hour mark almost engineered a fourth for the home side as Wilkinson held up long enough to pick out McAulay on the opposite side, but the angle narrowed on the Scotland international and Currie was able to block at her near post.
Berry ought to have extended the scoreline moments later when substitute Fallon Connolly-Jackson stole possession high to release the forward, but with only Currie to beat the teenager was denied by a sprawling save.
With 15 minutes remaining, the crowd rose to their feet to welcome both Laura Rafferty back into the action and a senior debut for midfielder Coyle-Morrow.
The latter stages then saw another debutant in forward O’Brien who replaced Wilkinson as Rangers saw out the victory to seal their place in the semi-final draw.
RANGERS: Fife, Austin (Connolly-Jackson, 51), Eddie (Rafferty, 74), Pegram, Docherty, McLeary (Coyle-Morrow, 74), Sabajo, Lafaix (Cruft, 45), McAulay, Berry, Wilkinson (O’Brien, 86)
Subs not used: Ivarsdottir, O’Donnell
PARTICK THISTLE: Currie, Slater, Handley, Falconer, King, Rennie (Syrjanen, 69), Donaldson, Fraser, Ferguson, Tweedie, Robinson (English, 12)
Subs not used: MacNair, McCulloch, Turner
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