Burgin (7-7) found its way back to .500, snapping a three-game losing streak.
The Bulldogs maintained a slim lead over Casey (6-8) for most of the second half, though they were able to stretch it to seven points late in the game.
"I think we made some poor decisions down the stretch with the basketball, and we got caught playing from behind," Casey coach Shawn Conley said. "We had a hard time making that little, tiny run we had to make to get some separation from a team playing at home."
Casey led for only 17 seconds after halftime, and Irvine said Burgin's pressure defense may have taken a toll on the Rebels in the fourth quarter.
"Sometimes our pressure makes people tired, and they looked a little tired," Irvine said. "I think that caused them to miss shots and gave us an opportunity to keep the lead. If we lost the lead in a game like this, that would be crucial."
Harris helped the Bulldogs keep the lead, going 6-for-8 from the field and 10-for-12 at the free-throw line in the second half. He was 7-for-9 and 11-for-13 overall, and he said it was just what he needed to get out of a slump.
"We haven't had a good matchup here lately that we could just ride him with," Irvine said.
Harris was matched with Casey's freshman center, Keith Price, who had 11 points and 11 rebounds but fouled out with 4:09 to play.
"I knew I could draw a foul if I needed to," Harris said.
Sean Bottoms was Burgin's best offensive weapon in the first half, when he scored 12 of his 18 points.
"I thought he gave a tremendous effort in the first half," Irvine said.
Freshman helps Bulldogs gain rebounding edge
Burgin also held a 37-35 edge on the boards thanks in large part to the efforts of freshman Daniel Loane, who had nine rebounds in the first half and finished with a career-high 12 boards.
"He stepped up big for us," Harris said. "We need somebody to come off the bench and give us good minutes like that, and he went to war on the boards for us."
"We needed every one of Daniel's rebounds," Irvine added. "He did an excellent job for us on the boards tonight."
Loane's only basket of the game came when he broke free for a layup to give Burgin a 55-48 lead. It followed a trip in which Casey missed two 3-pointers, either of which would have pulled the Rebels within two points.
The Bulldogs then hit six of 10 free throws in the final minute of a game that had seven ties and 12 lead changes. They were 17-for-27 overall at the line, while Casey was just 9-for-18.
Burgin shot 40.8 percent (20-for-49) from the field; Casey shot 37 percent.
The Rebels got 18 points from Charlie Fox, who was 4-for-12 from 3-point range, where Casey was 7-for-23 overall. Dustin Johnson added 17 points, all in the second half.
Casey was playing its first full game without senior Derek Vest, who suffered a partially torn anterior cruciate ligament in his knee Saturday against Danville. Conley said Vest will try to return to finish his senior season - he can play until the ligament tears completely - and could be back in as soon as three weeks if his rehabilitation efforts go well.
CASEY (6-8) - Charlie Fox 18, Keith Price 11, Dustin Johnson 17, Corey Dial 4, Jason Sanders 6.
BURGIN (7-7) - Joe Harris 25, Daniel Howard 2, Bobby Wylie 2, Zack Gross 11, Sean Bottoms 18, Daniel Loane 2.