Barthel, who thrashed Urszula Radwanksa of Poland in the first round, recovered from a set down to beat Vinci in 86 minutes.
The German, ranked at number 45 in the world, will next take on either third seed Marion Bartoli in the third round after the home hope crushed Christina McHale of the USA 7-5 6-1
Former Wimbledon champion Petra Kvitova also made it through, ousting Stefanie Voegele 7-6(5) 6-3 in an 84-minute encounter.
Kvitova, now ranked eighth in the world, has struggled with confidence in 2013, but held her nerve at the crucial moments, despite winning just 68 points in the match to her opponent's 74.
In first-round action, sixth seed Lucie Safarova, the world number 18 from the Czech Republic, also recovered from a set down to beat Lourdes Dominguez Lino of Spain 2-6 6-1 6-1.
WTA Paris results
Mona Barthel (Germany) beat 5-Roberta Vinci (Italy) 4-6 6-1 6-3
2-Petra Kvitova (Czech Republic) beat Stefanie Voegele (Switzerland) 7-6(5) 6-3
3-Marion Bartoli (France) beat Christina Mchale (U.S.) 7-5 6-1
6-Lucie Safarova (Czech Republic) beat Lourdes Dominguez Lino (Spain) 2-6 6-1
Magdalena Rybarikova (Slovakia) beat Virginie Razzano (France) 6-4 3-6 6-3
Yanina Wickmayer (Belgium) beat Anastasia Pavlyuchenkova (Russia) 7-6(7) 4-6 6-3
Kiki Bertens (Netherlands) beat Tamira Paszek (Austria) 6-4 7-5