The seventh-seeded Rus rallied for a 2-6, 6-3, 6-1 win against Australia's Daria Saville on Friday.
Noha Akugue, a 19-year-old qualifier competing in her first WTA main draw, defeated Russia's Diana Schnaider 6-3, 6-3 in 78 minutes in the other semifinal.
It will be the first WTA final between two left-handed players since Prague in 2018 when Petra Kvitova of the Czech Republic defeated Romania's Mihaela Buzarnescu in three sets.
Rus is the oldest first-time finalist since 34-year-old Tzipora Obziler of Israel at Guangzhou in 2007.
Follow the women's final at Hamburg on Flashscore.
Ladies Open Lausanne
Second-seeded Elisabetta Cocciaretto of Italy converted all seven break points and advanced to the semifinals in Switzerland with a 7-5, 6-3 win against Russia's Elina Avanesyan.
Cociaretto will next face unseeded Anna Bondar of Hungary, who blitzed Slovenia's Tamara Zidansek 6-2, 6-0 in one hour and 22 minutes.
Diane Parry and Clara Burel will meet in an all-French semifinal. Parry defeated countrywoman and seventh seed Alize Cornet 6-3, 6-2, and Burel was leading third seed Ana Bogdan 6-3, 1-0 when the Romanian retired.
BNP Paribas Warsaw Open
Germany's Tatjana Maria outlasted Slovakia's Rebecca Sramkova 6-3, 1-6, 6-1 to move into the semifinals in Poland.
The quarterfinal match between Italy's Lucrezia Stefanini and Germany's Laura Siegemund was interrupted by rain at 1-1 in the opening set, with the winner advancing to face Maria.
Maria saved four of eight break points and converted five of her 12 break chances against Sramkova, who hurt her cause with seven double faults.
