The team of Barringer, Robbie Thomson and Roger Barron won the Pathways title at the Waverley Bowls Club's indoor rink.
Fairfield remained unbeaten when it beat the team of Ray Martin, Tim Toomey and Richard Corry (Victoria, Wellington) 24-5 in the last game.
Both teams were unbeaten before the fifth and final round; Fairfield jumped to a 14-0 lead on the first five ends and was never troubled after that.
Fairfield played 17 games to win the final that started when it won the Bowls Dunedin champion of champions triples title.
Fairfield won the round robin competition with 10 points and was followed by Victoria 8, Tauranga South 4 (minus 8), Rangiora 4 (minus 9), Palmerston North 2 (minus 13) and Maungatapere, Northland 2 (minus 20).
Barringer was a rejuvenated bowler when he returned to the sport last summer, winning the Bowls Dunedin open fours and champion of champions triples to take his total of centre titles to eight.
He was also named the Bowls Dunedin male bowler of the year.
The tenacious Robbie Thomson was runner-up in the bowler of the year competition.