Glawe, a senior, hit 14-of-26 from the floor and 4-of-6 at the line. He added nine rebounds, four assists, five steals and two blocks.
It was a tight contest throughout, with the Rebels trailing 31-30 at the half. They led 40-38 after three.
Tim Saunders followed with six points and four rebounds for the Rebels. Christian Sylvester had five points and five steals, Dallas Hueton had four points and three rebounds, Colton Miller had four points, and Chris Ripke had two points and three boards.
The Rebels hit on 21-of-42 from the floor, 1-of-8 from three and 10-of-13 at the line. Sioux Central matched the taller Hartley-Melvin-Sanborn team on the boards, 22-22.
The Hawks (3-5) were led by Blake Simon's 23 points and six rebounds.
Jordan Japenga added eight points and Cade Harvey had six points, five rebounds and three assists.
The knocked down eight threes on 16 attempts to keep the contest tight. They 18-of-41 from the floor and 6-of-11 at the foul line.
"Very pleased with the effort of our guys," said Sioux Central head coach Steve Tjaden. "Our guards made great decisions with the ball and Glawe played as good as he has all year. Even though we were undersized, I felt we wre the more aggressive players and gave great effort in the last four minutes of the game."
The Rebels move to 2-6 with the win and will be on the road at Newell-Fonda Tuesday. They return home Friday night to take on Southeast Webster Grand.