Ligue 1 sides Ajaccio and Reims were dumped out of the Coupe de France on Saturday, with Evian only just escaping.
Ajaccio needed an 88th-minute equaliser from Wilfried Zahibo simply to force extra-time against Rouen, their third-tier opponents having led after Zahir Zerdab won and hammered home a 63rd-minute free-kick.
But Rouen won 3-2 on penalties, Theo Defourny with the decisive save from David Gigliotti after Julien Jahier scored Rouen's fifth penalty.
Evian almost suffered the same fate, only edging past fourth-tier Amiens on spot-kicks after leaving it even later in normal time.
Elhadji Mady Keita fired Amiens ahead and was only denied a second by a brilliant save from Bertrand Laquait before Evian equalised through Aldo Angoula deep in injury time and won 5-3 on penalties.
Reims, meanwhile, suffered a 1-0 defeat to fourth-tier Plabennec, Steven Coat with the only goal in the 27th minute. Lille held off a second-half fightback to beat Nimes 3-2.
A strong Lille side led 3-0 after 52 minutes thanks to goals from Dimitri Payet, Florent Balmont and Nolan Roux, but replies from Vincent Gragnic and Seydou Kone made for a nervous Grand Stade Metropole in the last 20 minutes.
There were 1-0 wins on the road for three other top-flight teams, Sochaux, Toulouse and Troyes.
Substitute Sloan Privat saw Sochaux past fifth-tier Thaon, seizing on a defensive lapse to score with a deflected shot in the 74th minute.
Emmanuel Riviere's 59th-minute goal earned Toulouse victory away to Ligue 2 Boulogne, and Troyes edged out Montceau thanks to Fabien Camus' 40th-minute free-kick.
Nancy, bottom of Ligue 1, took the opportunity of some light relief in the cup with their first win since the opening day of the season.
Benjamin Moukandjo eliminated any threat of an upset against fifth-tier Dreux with two goals in the first 10 minutes, and Djamel Bakar and Thomas Ayasse made it 4-0 at half-time.
There was understandably little urgency from the top-flight side in the second period and Hicham Tabate pulled a goal back, but Paul Alo'o Efoulou made it 5-1 in stoppage time.
Lorient downed Chauray by the same scoreline, Julien Quercia scoring twice. Le Mans were beaten 2-1 by Le Poire, with Kevin Lefaix netting a late winner, and Riyad Mahrez and Walid Mesloub scored in injury time to earn another Ligue 2 side, Le Havre, a dramatic 3-1 win at Belfort.
Elsewhere, there were wins on penalties for Moulins, Venissieu and Vertou in their respective away ties against Marseille Consolat, Savigneux Montbrison and St Malo.
Raon-l'Etape beat Amneville 2-1 thanks to an extra-time winner from Tresor Nyamwisi, Amneville having forced extra-time with a late Mohamed Belameiri penalty, while Baldy Dia's goal earned BordeauxStade a 1-0 win over Carquefou.