Bristol narrowly had the upper hand 98-94 when the two sides met in the league only two weeks earlier.
However, Newcastle enjoyed a dominant first quarter to take 31-19 lead, with Okauru scoring 17 of his 19 points, and remained in front the rest of the match, watched by more than 8,500 fans.
They stretched that advantage to 52-31 by half-time and although the Flyers outscored them in the final quarter by four points, their comeback attempt came too late.
“From top to bottom, the fans, the players, the city, the organisation, amazing, this means everything for our organisation. I’m elated,” Steutel told DAZN Sports.
Flyers guard Evan Walshe told BBC Radio Bristol: “We really wanted to do what was right for the city and bring a championship back, and we fell short, which really hurts.
“We have to find a way to pick ourselves up, we have a long season ahead and still have chances of more silverware.”