Ruse won her first WTA title at the Hamburg European Open in July and reached the final of the Palermo Ladies Open later that month, but she was second best against Halep.
The No.1 seed produced a commanding performance as she held serve throughout and broke her opponent twice in both sets to progress 6-1 6-2 in a time of 73 minutes.
Halep, who departed at the quarter-final stage of the Kremlin Cup last week, is on course to meet US Open winner Emma Raducanu in the semi-finals in Cluj.
Anett Kontaveit also prevailed on Thursday (AEDT) with a straight-sets win of her own, the No.2 seed seeing off Aleksandra Krunic 6-3 7-5.
The 25-year-old, seeking her third WTA 500 indoor trophy in the space of two months, made the most of some Krunic errors to set up a last-16 tie with Alison Van Uytvanck.
Anhelina Kalinina earlier beat Anna-Lena Friedsam 6-2 6-2 to become the first player to book their place in the quarter-finals.
At the Courmayeur Open in Italy, No.1 seed Dayana Yastremska required three sets to overcome Kateryna Kozlova 6-1 3-6 7-5.
Clara Tauson and Ann Li also avoided upsets as they beat Giulia Gatto-Monticone and Kamilla Rakhimova respectively.