Griffiths played a full game, but things started badly with Heracles going ahead through Iliass Bel Hassani in the 32nd minute. The home side's response was almost immediate however as Edwin Gyasi levelled four minutes later.
Tom van Hyfte put Roda ahead in the 49th minute, with Hicham Faik applying gloss with the third goal after 90 minutes.
Dirk Kuyt marked his return to Eredivisie action with the decisive late penalty as 10-man Feyenoord began the season with a 3-2 win over FC Utrecht.
Former Liverpool and Fenerbahce man Kuyt has been away from De Kuip for nine years but was brought back this northern summer by new boss Giovanni van Bronckhorst.
He put away the 82nd-minute spot-kick that gave Feyenoord a 3-1 lead, ensuring the Rotterdam side would come out on top.
Colin Kazim-Richards put Feyenoord ahead in the 23rd minute, but it lost Rick Karsdorp to a 51st-minute red card and was pegged back to 1-1 in the 75th minute by Sebastien Haller.
Tonny Vilhena restored Feyenoord's lead three minutes later, Kuyt soon doubled it, and Haller's last-minute penalty was a consolation for Utrecht.