Diacre became the first female coach to take charge of a professional male team in the top two divisions of a European nation when she oversaw Clermont's 2-1 defeat at Brest last week, a result which was followed by a 1-1 draw with Auxerre.
And her short winless streak ended on Tuesday as midfielder Pierrick Capelle netted after five minutes to ensure victory for Clermont against their third-tier opponents.
Sochaux and Valenciennes - relegated from Ligue 1 last term - both suffered the ignominy of early exits.
The former were beaten 2-0 at Laval, while Valenciennes were dealt a 3-1 loss by last season's semi-finalists Troyes in match that saw midfielder Eloge Enza-Yamissi sent off against his former club.
Striker Quentin Ngakoutou completed his hat-trick four minutes from time to give Arles an enthralling 3-2 win over Niort, who were eliminated despite Seydou Kone's double.
Meanwhile, Nancy overcame Le Havre 2-1, and Romain Thomas' injury-time strike sealed a 2-1 success for Angers versus Nimes.
Creteil progressed with a 2-1 away triumph at CA Bastia after extra time, while three ties went to penalty shoot-outs.
Gazelec Ajaccio emerged victorious on spot-kicks at Brest, who had claimed a 1-1 draw in normal time thanks to an injury-time leveller from Bruno Grougi.
Elsewhere, Dijon and Auxerre won on penalties at Tours and Orleans respectively.