Anderson tossed in 13 points for Flippin, while Barrow added 12.
However, what the fourth-seeded Bears could not overcome was their second straight game of double-digit (22) turnovers.
Those miscues helped fifth-seeded Flippin push past Mammoth Spring 48-42.
The Bobcats got off to a good start and held Mammoth Spring to just 11 points in the first half of play.
Barrow hit two treys late in the first to help the Bobcats to a 13-5 lead after the first period.
Flippin extended that lead to 17-5 early in the second, before Caleb Brown hit a free throw for the Bears' first points of the second. Brown paced Mammoth Spring with a 15-point, 12-rebound double-double.
The Bears' only other points in the second came from a Houston Cooper (eight points) free throw and two hoops by Wes Coffey (nine points), leaving Flippin with a 23-11 lead at intermission.
Mammoth Spring found a little bit of its stride in the third period and made things difficult for the Bobcats.
Brown ripped off eight straight points for the Bears and Wes Coffey racked up a rare four-point play with 2:20 left in the frame to pull Mammoth Spring within four, down 27-23.
But Colbie Butcher responded with a pair of big 3-pointers in the last two minutes of the stanza, helping to keep Flippin in front 35-26 heading into the final frame.
Mammoth Spring pulled within five points in the fourth, but even though Flippin had a bout of shaky free throw shooting deep in the frame, the Bobcats still managed to hold off Mammoth Spring for a 48-42 victory.
Austin Hite finished with four points for the Bears, while Chris Young added three and Wayne Coffey two.
In the opening round Jan. 7, the Bears edged past the Norfork Panthers 48-44.
Mammoth Spring overcame 22 turnovers in the game by shooting 10-of-13 from the charity stripe in the fourth period.
Wes Coffey paved the way with 17 points, while Caleb Brown tacked on 16 points.
The junior Bears were knocked out of the first round of the Screamin' Eagle Junior High Tournament with a 50-36 loss to the host team from Hillcrest Jan. 9.
Matt Turnbough paced Mammoth Spring with 14 points.
A.J. Smith and Craig Hoover added nine points each for the junior Bears.