Griffin threw two touchdown passes while running back Roy Helu also went in for three touchdowns in a dramatic match that saw the Redskins take the lead on no fewer than six separate occasions.
The 23-year-old admitted that it wasn't a perfect performance by his side, but he does believe that they did enough to warrant the win.
"When we go watch the film we won't watch it with smiles on our face. But I think we made enough plays today to win the game, and that's all matters," Griffin told The AP.
Last season's Offensive Rookie of the Year also revealed that he made a mental breakthrough during the match, having started the season slowly following his recovery from a serious knee injury in the last campaign.
"I think mental part of it that I did get over was not thinking out on the field, just reacting. And I don't think that was anything to do with my knee, the knee brace or anything else, I just think that was for me mentally playing the game irrelevant of my injury," he added.
The Redskins remain third in the NFC East following the win, which improves their overall record to 2-4.