The victory gave BB&O the crown at Robin Hood GC, Solihull, while Yorkshire - who had been edged 5-4 by Devon in their second match - placed third.
At the start of Thursday’s play Yorkshire, BB&O and Devon were all in with a chance of winning the title, but the eventual champions started as favourites, knowing that a halved match or better against John Grimbleby’s side would give them victory.
Their mastery of the fast greens helped them to a perfect score of three wins from three matches.
They took the morning foursomes 3-0 although Yorkshire seniors champion Stephen East and partner Peter Ward only succumbed at the final hole to East’s fellow England senior internationals David Niven and Andrew Stracey.
The momentum was with BB&O and a whitewash appeared possible, but East, with a victory, and Ian Clarke, with a half, put 1.5 points on the board for the White Rose in the afternoon singles.
In the day’s other match, Devon beat Worcestershire 6-3 and finished the event as runners-up.
“This is the holy grail of senior golf,” said BB&O captain Ashley Brewer, whose team were making their first appearance at County Finals.
“BB&O have been trying to win this ever since it started, but there are stronger counties in the South East and we have been second seven times in qualifying. To have finally got past our nemesis, Kent, by 22 shots in qualifying and to play at the magnificent Robin Hood Golf Club was our chance.”