Nice were reduced to 10 men on the stroke of halftime when Olivier Boscagli was sent off before Bernardo Silva and Layvin Kurzawa turn things around after Valere Germain's early opener.
Promoted Angers are the early leaders after Abdoul Razzagui Camara and Gilles Sunu gave them a 2-0 win at Montpellier, while Olympique de Marseille lost 1-0 at home to Caen.
At Nice's Stade du Ray, Germain, on loan from Monaco, opened the scoring with a close-range half volley after seven minutes, before Nice lost Boscagli in the 45th for a second yellow card.
Stephan El Shaarawy, on loan from AC Milan, was brought on shortly before the break but it was Bernardo Silva who levelled as he coolly slotted home eight minutes into the second half.
Left back Kurzawa's 64th-minute header then smashed against the bar but the ball bounced back into his path and this time he nodded it into the net.
El Shaarawy came close to scoring but his fine overhead kick was tipped over the bar by Mouez Hanssen.
Marseille, without top signings Abou Diaby and Lassana Diarra, suffered disappointment despite dominating against Caen, who went ahead when forward Andy Delort's missile from outside the box beat Steve Mandanda in the 27th minute.
Michy Batshuayi had what he thought was an equaliser ruled out for offside in the 36th as OM piled on the pressure but Marcelo Bielsa's team missed scores of chances after the interval and were booed off their Stade Velodrome pitch.
On Friday, champions Paris St Germain beat Lille 1-0 away despite being down to 10 men from midway through the first half.
Last year's runners-up Olympique Lyonnais start their Ligue 1 season on Sunday at home to Lorient.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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