It was a relentless display from Malky Thomson’s side who had a 6-0 lead at the break thanks to doubles from Kirsty Howat and Jodi McLeary, a Lizzie Arnot penalty and a fantastic strike from Megan Bell.
Brogan Hay, Jodi McLeary, Emma Watson and two from Jenny Danielsson added to that in the second-half as Rangers booked their place in Monday’s draw.
Victoria Esson started in goal with Nicola Docherty, Kathryn Hill, Lisa Martinez, and Rachel McLauchlan in front of her.
Kirsty Maclean was joined in midfield by Colette Cavanagh and Lizzie Arnot, while Megan Bell made her first start of the season having returned from injury, with Jodi McLeary and Kirsty Howat completing Rangers’ line-up.
Gers started well as they looked to take control of this cup tie and had an early sight of goal as Megan Bell’s cross met Lizzie Arnot in the box but her header was just over the bar.
However, it wasn’t long until the Light Blues had the breakthrough with Kirsty Howat opening the scoring in the 5th minute. It was a well-worked goal from Rangers as Lizzie Arnot played a short corner to Rachel McLauchlan with the full-back taking a touch beyond a Stirling defender before whipping a ball into the box.
Howat had made a driving run to the back post to get on the end of the ball and slot home beyond Leigh Skelton.
Rangers had a fantastic chance to double their advantage as Jodi McLeary got on the end of a ball from Colette Cavanagh but Skelton was able to get enough on the close-range effort to turn it behind for a corner.
With 14 minutes on the clock, Rangers' dominance paid off as they got their second goal of the afternoon. Skelton pulled off a good save to deny Colette Cavanagh but Jodi McLeary was alert to the rebound to slot beyond the goalkeeper.
Howat had a chance cleared off the line by Rebecca Hellgren as Rangers continued to pile the pressure on the visitors before Megan Bell made it three with a fantastic strike in her first start of the season.
The winger found space midway into the Stirling half and decided to take on the shot as she released a terrific long distance strike which looped over Skelton and landed in the back of the net.
As the game approached the half-hour mark, Rangers made it four. Lizzie Arnot put pressure on the Stirling defenders and managed to deliver a good ball into the box which Jodi McLeary guided beyond Skelton for her second goal of the afternoon.
Rangers were relentless and were awarded a penalty as they looked to threaten the Stirling goal once again with Kirsty Howat brought down by Lucy Jackman. Lizzie Arnot stepped-up to the spot and sent a powerful right-footed shot low into the bottom corner of the net to give Rangers a five goal advantage.
Howat got her second of the afternoon in the 38th minute as Rachel McLauchlan picked out the striker in the box and she hit a composed finish beyond Skelton.
Late in the first-half, Colette Cavanagh was denied by the post as she looked to get on the scoresheet this afternoon.
Malky Thomson made two changes to his side at the break as Nicola Docherty and Lizzie Arnot were replaced by Brogan Hay and Emma Watson.
Rangers started the second-half the same as they ended the first and it wasn’t long until Hay got herself a goal. With 54 minutes on the clock, Rachel McLauchlan again provided the assist as she found Hay at the back post and the winger made no mistake in turning home to increase Rangers’ advantage.
On the hour mark, Thomson made three further changes to his side as Chelsea Cornet, Jenny Damielsson and Tessel Middag were all introduced in place of Rachel McLauchlan, Kirsty Maclean and Megan Bell.
Jodi McLeary had her hat-trick in the 62nd minute as she got on the end of a good ball from Emma Watson. McLeary’s initial shot was blocked by Skelton but the youngster made no mistake second time around as she touched it beyond the goalkeeper.
Shortly after, it was 9-0 as Emma Watson became the sixth Rangers goalscorer of the afternoon. Kirsty Howat played a lovely weighted through ball into the path of Watson who had made a driving run into the box and it was a fantastic finish from the 16-year-old as she lifted the ball high into the back of the net.
With eight minutes of the game remaining Rangers hit 10 as Finland international Jenny Danielsson showed her quality in the box as she created space for herself before slotting beyond Skelton.
Danielsson got her second goal of the afternoon shortly after as she stuck a low shot from the edge of the box into the back of the net to round of the scoring for the afternoon.
RANGERS: Esson, Docherty (Watson, 46), Hill, Martinez, McLauchlan (Cornet, 61), MacLean (Danielsson, 61), Cavanagh, Arnot (Hay, 46), Bell (Middag 61), McLeary, Howat.
Subs not used: Fife, McCoy, Kerr.
Stirling University: Skelton, McKay, Watson, MacPhail, Lyons, Taylor, Varnava, Hellgren, Fairgrieve, Davidson, Kennedy.
Subs: Baker, Jackman, Kerl, Gullan, Harper, Salmond, Hope, Ryshchina