Smith was the best of his team in the crucial final round when he carded a one-under par 71, with Edwards (73), Beard (74) and Sam Davis (75) in the format where the best four out of five scores counts towards the team total.
The win is Bay of Plenty's fourth (2001, 2003, 2006 and 2014) since the event began in 1977 and their first in eight years.
Davis (Tauranga) said the team learned a huge amount about their resolve in the testing conditions.
"The key in those conditions was hitting it to spots where you can make birdie and, if you don't, then you have to scramble well to make your par," he said. "Those conditions test your character because you are going to hit bad shots and it is all about how you respond to that."
The stage is now set for what will be an intriguing Toro NZ Men's Interprovincial at the St Andrews Golf Club in Hamilton from December 2-6.
Bay of Plenty, who won the title in 2012 and were beaten finalists at North Shore in 2013, will now head to Waikato with plenty of confidence.
"It's been a good team bonding experience," said Davis. "It was good to spend some time together."