The All Blacks ran in four tries to claim a 24-13 bonus point triumph and a third straight victory over their Shropshire rivals.
It was a result which saw them stay fourth in the Midlands Premier Division, now eight points ahead of sixth-placed Newport.
Griffiths said: “It’s a match we always circle as a highlight on the fixture list. There is always a bit of added spice.
“Newport have always addressed themselves as the premier rugby club in the county and are quite happy to tell people that.
“At one point last season I think they referred to us as the noisy neighbours. It is nice for us to just to keep our heads down and keep pushing them back.”
Newport took the lead through an early penalty but it was Bridgnorth who were in command and they went ahead when Gareth Bladen crossed for the first try of the match, Llew Williams adding the conversion.
Jonah Boyce then scored just before half-time to make the score 12-3 and it was the All Blacks who remained on top during the second half.
Former Newport centre Ricky Bailey burst through to leave his former club in an even bigger hole, before Joe Cave scored to secure the bonus point. A late try for the home side proved merely a consolation.
“We just controlled the game,” said Griffiths. “It turned into a bit of an arm wrestle and we ended up the stronger unit. I was really pleased with the way we conducted ourselves.
“The only time they broke our lines all afternoon was with two minutes to go. That was the only time our concentration slipped.”
The win extended Bridgnorth’s unbeaten run to seven matches, continuing their impressive resurgence since losing the opening two games of the season.
After an impressive fifth-placed finish last term, Griffiths believes they have the potential to go even further this time around.
“We are definitely targeting a top three finish. At the moment we are 10 points behind Bournville at the top of the table but we still have to play them at home.
“We had a bit of a sticky start but since then we have started to improve and I have been really pleased with our performances.”