Bogan, the Cubs 6-foot-10 junior center, scored a game-high 33 points and Niemczyk added 27 as the Cubs used superior height, depth and experience to dismantle the younger Braves.
Bell City, the state's third-ranked Class 1 team, overpowered Scott Central on the boards by a huge 44-23 margin.
"Rebounding. That was mission No. 1 coming in," said Bell City coach Brian Brandtner.
Bogan, who dominated the middle with 13 rebounds and senior forward Jeff Liggins with 10 equaled the Braves' board production. Bogan grabbed eight offensive boards, resulting in several easy putbacks.
"He's a matchup problem for everybody," said Scott Central coach David Heeb, of Bogan. "He's a good player. He's not just big, he's good and when a good big kid plays against six-foot players, that's what he should do. Give him credit for doing what he should do."
Bell City (26-4) opened an 18-10 first-quarter lead on the strength of a 10-2 run late in the period and never looked back.
"They played well early which put us behind the eight ball and when you have to scramble and try to come back you're playing into their hands," said Heeb.
But underdog Scott Central (16-14) managed to hang around as they trailed by 12 at the half, 34-22.
Said Heeb, "I felt like we had played very poorly and were still in the ballgame."
But Bell City poured it on, outscoring the Braves 48-29 in the second half, behind Bogan's 23 and 16 from Niemczyk.
"At halftime, we look and we're not in foul trouble, so we know we're going to get after it and wear them down in the second half," Brandtner said.
The Cubs extended the lead to 56-39 as the third period expired.
"They (Scott Central) made a couple of runs at us but they looked tired to me so I didn't want to call any timeouts because I thought that might help them. They looked like they didn't have their wind and we just weathered the storm a couple of times and persevered."
Early in the final quarter, Bell City, with a 9-0 run, went up 65-39 over the weary Braves. Then with about 1:20 to go, Bogan's two free throws invoked the mercy clock with a 30-point lead at 81-51.
"We've got eight solid players and we're in great shape," said Brandtner. "I think that showed tonight. We had better legs maybe and that really helped us, especially in the second half."
Sophomore guard D.D. Gillespie topped the Braves' scoring with 17 points and sophomore forward Caleb Johnson added 12.
Bell City, with Bogan going 9-of-10 and Niemczyk 7-of-8, hit 18-of-24 free throws. Scott Central went 11-of-16 from the stripe.
The Cubs, a state semifinalist last season, advance to the quarterfinal round against Verona (23-6), a 44-40 winner over Eminence in its sectional.
The game is set for Saturday at 2:45 p.m. at the Civic Center in West Plains.
"I think we're starting to play our best basketball right now," said Brandtner. "We're starting to round into a pretty good ballclub."