Bogdan won a tightly contested second-set tiebreaker on her second set point, then rallied from down 5-4 in both the third set and the ensuing tiebreaker to finish the upset. Bogdan had eight aces without a double fault while saving 12 of 18 break points; Rus had four aces but committed eight double faults.
Bogdan will face countrywoman Jaqueline Cristian in the semifinals, ensuring one player from Romania will reach the final on her home soil. Cristian defeated Latvia's Anastasija Sevastova 6-3, 7-5.
The other semifinal will pit Great Britain's Harriet Dart against Karolina Pliskova of the Czech Republic. Dart beat Spain's Nuria Parrizas Diaz 6-3, 6-2, and Pliskova skated by Italian Sara Errani 6-2, 6-0.
Mubadala Abu Dhabi Open
Number six seed Beatriz Haddad Maia of Brazil felled second-seeded Ons Jabeur of Tunisia 6-3, 6-4 in quarterfinal action in the United Arab Emirates.
Despite Jabeur holding a 4-0 edge in aces, Haddad Maia prevailed by converting three of five break-point chances while saving four of the five break points she faced.
Top seed Elena Rybakina of Kazakhstan was more fortunate, as she cruised past Spaniard Cristina Bucsa 6-1, 6-4 in just 64 minutes. Rybakina's semifinal opponent will be Russian eighth seed Liudmila Samsonova, who was a 7-5, 6-4 winner over Czech fourth seed Barbora Krejcikova.
Haddad Maia will face Russian seventh seed Daria Kasatkina, who soundly defeated Romania's Sorana Cirstea 6-2, 6-0.
