Neal had 18 of his 21 points in the second half while Byrd added 14 of his 20 in the second half. Combined, they made 9 of their 11 shots in the second half, including all three 3-pointers and 10 of their 11 free throws.
Their efforts helped Butler hold off Garden City down the stretch. The Grizzlies had jumped out to a 6-0 lead, but Garden City scored seven straight to take the lead. The game went back-and-forth in the first half until Ken Perkins made a free throw to make it 26-25 with 5:35 left in the period.
Butler would lead by six after a Romales Walker 3-pointer made it 35-29 with 2:21 left in the half, but didn't score again and led 35-32 at the break.
In the second half, Garden City tied the game twice and then took a 48-46 lead with a 3-pointer by Josh Fleming with 13:36 to go.
Caelan Neal answered with a 3-pointer with 12:45 to go to make it a 49-48 Butler lead and the Grizzlies would not trail again.
The Grizzlies would take their largest lead after a 3-pointer by Derrick Byrd made it 64-56 with 5:38 to go, but Garden City again trimmed the lead down to two points with 1:32 to go.
Butler would hit seven of eight free throws in the final 75 seconds and outscored Garden City 9-5 in that stretch to secure the victory.
In addition to the 21 from Caelan Neal and 20 from Derrick Byrd, Butler got nine from Will Adler, seven from Damien Akao and six each from Ken Perkins, Romales Walker and Darrell Jacob. Calean Neal also led Butler in rebounds with eight, while Akao had six.
Butler has now won nine in a row to improve to 9-3 on the season and 1-0 in Jayhawk Conference play. The Grizzlies have also won 26 consecutive home games dating back to 2014.
The Grizzlies will be at home on Saturday to take on Barton at 4 p.m. The Cougars won 68-52 at Pratt on Wednesday and are also 9-3 overall and 1-0 in conference.