France striker Griezmann struck early on as he netted in three consecutive games for the first time in a Barca shirt.
Martin Braithwaite and Ousmane Dembele were also on the scoresheet for Barcelona, who had already qualified for the competition's knockout phase.
The victory also ensured Barca won their first five Champions League group stage games for the first time since the 2002-2003 campaign and it lead second-placed Juventus by three points with one match remaining.
Lionel Messi was rested by Barcelona coach Ronald Koeman for the trip to Hungary but without the influential Argentina international his side played some superb football.
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.
The 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.