Stanley scored three goals in the first half to secure their first win in five games and add to relegation-threatened Bournemouth's problems.
The home side opened the scoring with the first attack of the game when Gornell threaded the ball through for striker Mullin to slot home his fifth goal of the season in the third minute.
Accrington doubled their advantage in the 13th minute when Gornell's shot took a deflection and looped over Cherries goalkeeper Shawn Jalal and into the net.
A rampant Stanley made it 3-0 seven minutes later when on-loan midfielder Griffiths unleashed a thunderbolt into the roof of Jalal's net from 20-yards out to score his first goal for the club.
Veteran midfielder Darren Anderton fired over and Michael Symes flashed a shot across the goal, while defender Jason Pearce missed an open goal as Bournemouth's struggles continued.