Razzano, 31, already beat Niculescu once previously in 2014 in qualifying for Paris' Open GDF Suez, and repeated the feat on her home soil once more in France - winning 4-6 6-4 6-3.
Earlier in the season, there was just 31 spots between the pair in the rankings, but Razzano's slide to world number 172 in the world made her victory at the WTA 125K event all the more meritorious.
Seventh-seeded Swiss Stefanie Voegele survived an early scare to book her place in the second round with a 4-6 6-1 7-6 (10-8) win against Czech Katerina Siniakova.
Despite not being seeded, Siniakova is ranked four places higher than Voegele and instantly gave the Swiss cause for concern with a break of serve in the first game.
Voegele restored parity with an immediate break back, but let her guard slip again to go 4-3 down, subsequently losing the set.
The players exchanged breaks again at the start of the second set, before Voegele stormed to five games in a row to pull level.
The decider reflected the duo's proximity in the women's rankings, with Voegele eventually edging the match in an extended tie-break to set up a clash with Dutchwoman Richel Hogenkamp in the next round.
Aliaksandra Sasnovich of Belarus was sent packing by French ninth seed Kristina Mladenovic, who won 7-5 6-3, Ukraine's Lesia Tsurenko progressed past Russian Darya Kasatkina 6-7 (4-7) 6-4 6-0, and Montenegro's Danka Kovinic suffered an unexpected loss at the hands of another Ukrainian Maryna Zanevska 6-0 6-4.
Fifth-seeded Slovak Anna Schmiedlova did not drop a game as she progressed, after Romania's Andreea Mitu retired after losing the first set 6-0, while Kazakh Yulia Putintseva downed French wildcard Amandine Hesse 6-3 6-4.