Rangers thrashed Aberdeen 10-0 at home in the league in February and 11-0 away from home in August.
SWPL leaders City, who last lifted the trophy in 2019 and last reached the final in 2022, needed extra-time to overcome Heart of Midlothian, who sit fifth in the top flight, 3-2 away from home.
Opponents Motherwell, who were losing finalists in 2018 and currently lie sixth in the SWPL, eased through 3-0 away to second-tier Boroughmuir Thistle.
City won their most recent league meeting with Motherwell 4-0 at Petershill this month and also prevailed by a single goal away from home in September.
The semi-finals at Hampden Park are due to be played on the weekend of Saturday 26 and Sunday 27 April.
