An Abercrombie three started the score rolling for the Breakers who trailed narrowly, 24-23 at quarter time.
Scoring slowed in the second period but with 8 points from Webster and 6 apiece from Abercrombie, Loe and Vukona the scores were locked 37 apiece at halftime.
A highlight of the half was Brisbane swingman Torrey Craig leaping over the scorebench officials in an attempt to execute an intercept.
The Breakers suffered a blow early in the second half when centre Rob Loe had to sit down after picking up his fourth foul. With Vukona also in foul trouble it was left to rookie Finn Delany and new man Mitchell to battle the experienced Brisbane front court.
Despite three points and a shuddering block from Mitchell, the Breakers found themselves trailing 57-45 with three minutes remaining in the period and needing a timeout.
A trio of free throws from Isaih Tueta, another basket from Mitchell, and Webster in transition, saw the deficit reduced to 59-52 at three-quarter time.
Four minutes into the final quarter the Brisbane lead was twelve points, 68-56.
Despite an And 1 play from Woodside and a triple from Webster the visitors still held sway, 75-65, as Vukona fouled out with three minutes to play.
Mitchell demonstrated he is a fine addition to the Breakers roster with two late baskets but the Bullets lead was never threatened as they eased to a ten point win.
The two teams will meet again in Napier on Thursday needing to address the rebounding count (39-25 in favour of Brisbane) and the perimeter shooting (6 from 28 at 21%). The third and final hit out is in Invercargill on Saturday.
The Breakers arrived in Tauranga at lunchtime on Monday and undertook a series of community events in the two days leading into the game.
The players visited a number of local schools including Aquinas College, Bethlehem College, Mount Maunganui College, Mount Maunganui Intermediate and Te Akau Ki Papamoa Primary.
Breakers 70 - Mitchell 15, Webster 13, Abercrombie 11, Tueta 8, Woodside 7, Loe 7
Brisbane 80 - Craig 20, Young 12, Jervis 12, Petrie 10