Raducanu, who was the surprise US Open champion in September after not dropping a set throughout the tournament, appeared at just her fourth tour-level tournament and came to Cluj as third favourite.
The 18-year-old had lost opening-round matches at previous events in Nottingham, San Diego and Indian Wells.
However, world number 23 Raducanu finally recorded her first victory as she overcame a first-set scare to triumph over Hercog 4-6 7-5 6-1.
In the opening match of Tuesday's fixtures, sixth seed Marta Kostyuk cruised past Bernard Pera 6-3 6-4 to secure her last-16 berth.
Irina-Camelia Begu, ranked one behind Kostyuk for the tournament, did not enjoy similar fortunes as Romanian compatriot Irina Bara triumphed 7-6 (7-2) 0-6 6-4.
Jaqueline Cristian survived a marathon slog against Kaja Juvan as she came from a set down to win 3-6 7-6 (10-8) 7-6 (7-3) and book a second-round meeting with Ajla Tomljanovic.
Number one seed Simona Halep – who departed at the quarter-final stage of the Kremlin Cup last week – plays her first game on home turf on Wednesday against Elena-Gabriele Rusa and could meet Raducanu in the semi-final stages.
Meanwhile, Liudmila Samsonova, the third favourite at the Courmayeur Open, cruised past Stephanie Wagner 6-3 6-0 while seventh seed Jasmine Paolini comfortably dispatched Martina Di Giuseppe 6-4 6-1.
Shuai Zhang, who is the third seed in Italy, also enjoyed a routine victory as she eased past Jessica Pieri 6-1 6-3 after fourth favourite Petra Martic crashed out 3-6 4-6 to Saisai Zheng.