Tries from Taylor Buller and a penalty try sealed the points for Albion, while Stu Heal added 13 points from the kicking tee.
Harry Autun crashed over for Pethy while Harry Roberts kicked five points.
On a day that saw over 1,000 people pack the stands at College Way, Innalls was full of praise for his forwards and said his side are now 'full of confidence.'
He said: “We're very pleased with the win and it was a good performance in front of a massive crowd. I thought we should have beaten them earlier in the season but they just snuck away from us, but this time I thought we totally deserved it.
“The pitch was a bit greasy as you can imagine, but our forwards were dominant in all areas of the game. Although it was wet and greasy, when we got the chance we tried to play a bit and we defended really well as well, I thought the win was well deserved.
“It was a great day for the club and the clubhouse was so busy after the game. We had the sponsor's dinner before the game and neither club's second, third or colts had a game, so they were all watching as well.
“It was a long night at the club and everyone had a few drinks, it was a good day all round.”
North Petherton captain Sam Williams said his side were left 'gutted' at the result, but believed the better side won the game.
He said: “There's not a lot to say about it really. Bridgwater were the better side and wanted it more. I think the better team won on the day and they played the conditions better than we did.
“But we've got a big game at Camborne next week so we need to bounce back.”