France striker Griezmann struck early on as he netted in three consecutive games for the first time in a Barca shirt.
The victory also ensured Barca won their first five Champions League group stage games for the first time since the 2002-03 campaign and they lead second-placed Juventus by three points with one match remaining.
Barcelona’s opener came via Griezmann in the 14th minute, the forward elegantly backheeling in Jordi Alba’s low cross.
Koeman’s side increased their advantage moments later when Dembele unlocked the Ferencvaros defence with a jinking run before his cross was met by the sliding boot of Braithwaite to complete a 33-pass move.
The lively Braithwaite then won a penalty just before the half-hour after he went down following a slightly mistimed tackle by Abraham Frimpong.
Dembele confidently stepped up and sent Ferencvaros goalkeeper Denes Dibusz the wrong way with a clinical spot-kick.
Braithwaite tamely shot wide from a good position before the half-time break before Barcelona started to take things easy in the second half.
Dembele burst into life when he rampaged forward on a fine solo run, only to see his shot fly into the side netting.
France forward carried Barca’s main threat in the remainder of the contest and twice brought smart saves out of Dibusz late in the game, in a stylish win.