Despite a staunch defensive effort from Montpellier HSC, Olympique Lyonnais' star-studded squad proved just too much for them to handle.
The outsiders took an early lead through Alves before a fine Mbock finish levelled the scores immediately after.
Montpellier's defence looked to have seen them through to extra-time, only for Necib to score a stunner from range and ensure Lyon completed another double.
Level at half-time
It was a whirlwind start to proceedings in the showpiece fixture, as both sides scored within the opening four minutes. Andressa Alves gave Montpellier the lead with a superb break down the left. Lyon failed to clear the ball which bobbled across the face of goal, though Alves was on hand to rifle home from close range.
The league champions were hunting down the treble, however, and hit back immediately. Griedge Mbock Bathy was the unlikely scorer as she darted towards the near post and collected Camile Abily's cross. Mbock showed great skill to control and volley in one swift movement, finding the far corner in the process.
Lyon dominated proceedings after that, and even had a goal disallowed for a foul on Solene Durand. The Montpellier stopper was, however, in fine form as she did brilliantly to save from Eugenie Le Sommer's strong run and shot. Ada Hegerberg had been quiet in the early stages, and she thrashed a loose ball in the box over the bar.
Le Sommer then saw her superb finish chalked off for offside, as she tucked home from Abily's clever pass. It was proving to be a fantastic final but after goalscorer Alves went down with a nasty neck injury, focus quickly turned to her. After five minutes of treatment, Virginia Torrecilla replaced Alves as she was stretchered off.
There were further chances for Lyon to grab what would have been a deserved lead. Amandine Henry and Le Sommer both shot over from promising positions, while Wendie Renard's free header was straight at Durand. There was a reassuring sight as the teams came off for half time, as Alves was pictured on the bench.
Necib breaks Montpellier hearts
The second half was nothing like the first and, aside from Marie-Charlotte Léger's opportunity, it as a case of weathering the storm from a Montpellier point of view. Durand made a smart save with her legs and a few shots went well wide, in what was proving to be a frustrating afternoon for Lyon.
Lotta Schelin and Louisa Necib were both introduced in the second period, and the latter had the desired impact. A hopeful ball forward bounced between midfield and defence, but on the toe of Necib. It bounced kindly and she needed no second invitation to send a stunning half-volley over Durand to seal another domestic double.