Both got hard-earned wins Monday night and will host Region 1 satellite games Saturday night.
D-B (21-7) squeezed out a 58-55 victory over fired-up Volunteer in a game that almost became football at times.
Tennessee High (24-9) - its style a throwback to the 1950s - defeated longtime Big 9 Conference kingpin Science Hill 48-42 with a fast-moving zone and time-killing offense.
Coty Sensabaugh scored 16 points, Justin Sylvester 15 and Josef Throp 11 for D-B, which finished 10th in the final Associated Press Class AAA poll of the season.
D-B was inactive for nearly two weeks and it showed on the court.
"We had an 11-day break,'' Indians coach Charlie Morgan said. "We certainly have cooled off.''
Volunteer, the No. 5 seed, proved to be a formidable foe.
"I knew it would be a tough game,'' Morgan said. "You've got to watch out for a team with swagger. Volunteer plays very physical.
"I was concerned all week about our intensity, and it was down a bit.''
Sylvester clearly was the difference for D-B. He scored 10 points in the opening quarter, finished 6-for-12 from the field and came down with nine rebounds - six on the offensive end.
The 5-foot-10 sophomore has been a thorn in Volunteer's side this season.
"Sylvester was a big scorer against us all three times,'' Falcons coach Todd Whittemore said. "It was a blessing in disguise for D-B's team when Sensabaugh missed half the year with an injury - not for Sensabaugh, of course. But it allowed Sylvester to season out playing in Sensabaugh's place. This enabled Morgan to develop an extra player.''
Morgan agreed that Sylvester has been a spark.
"He plays a lot bigger than his height," the D-B coach noted. "Sylvester does a lot of things well for us. He has a knack for being around the ball.''
The layoff left some rust on the Indians, Sylvester said.
"It seemed like forever," he said of the layoff. "Hopefully, this was a game that got everything out. It was rough out there. Volunteer was after us.''
Chadd Browder scored 23 points and Keith Cradic 12 for the Falcons (20-11). Browder and Darren Mauk each claimed nine rebounds.
Each ballclub made only 40 percent of its floor attempts.
"Our shots weren't falling,'' Cradic said. "I don't think I hit a deep one. We didn't expect Throp to hit those jumpers like he did.''
If he could have, Whittemore would have lobbied for a 33-minute game.
"We just ran out of time,'' he said. "I'd like to have had just one more minute. You never know what might have happened.
"Our guys never quit," Whittemore added. "They have a lot of heart. We didn't get to the free throw line as much as we'd have liked to.''
Volunteer outrebounded D-B 34-31 but committed five more turnovers.
The Falcons will face Science Hill (28-7), the state's ninth-ranked team, in the consolation game at 6 p.m. on Wednesday. Both teams have qualified for Region 1 play and must travel Saturday for satellite action.
Against Science Hill, Tennessee High controlled the tempo with its methodic approach, taking high-percentage shots.
Corey Young, who had just two field goals, led the way with 16 points. He was 10-for-10 on the foul line.
As a team, Tennessee High hit 16 of 17 freebies.
"Somebody always steps up,'' Vikings coach Roby Witcher said. "That's the mark of this team.
"Belief is a huge thing in your mind. These kids believe they can win.''
Omar Wattad, Science Hill's all-time leading scorer, was held to a mere four points
"You can get good shots against that zone,'' Hilltoppers coach Ken Cutlip said. "We just missed them. We seemed a step slow.''