The lead changed hands a number of times before the Mariners took the lead for good in the seventh innings.
Kaz Rahman was crucial in their victory, collecting four hits in five.
He singled in the first, doubled in the third, singled in the fourth, singled in the seventh and walked in the eighth.
Plymouth Mariners had 28 hits in the game. As well as Rahman, Dan Brown, Keith Day, Greg Staniforth, Martin Mules, Daniel Herrera, Matt Vann and Stephen Dickson also collected multiple hits.
The Mariners did not commit a single error in the field. Mules had the most chances in the field with eight. Taunton Muskets collected 22 hits.