Anderson, the 6-foot-6 freshman, hit a career-best six three-pointers and scored a game-best 26 points, while Eaton, the junior point guard, scored all of his 14 points in the second half for the Cowboys.
The Cowboys, now 5-3, were in jeopardy of losing a non-conference home game for just the fourth time (in 144 contests) since 1987-88. East Tennessee State had taken a 63-59 lead on Courtney Pigram's jumper with 7:58 left to play.
But the Cowboys outscored the Buccaneers 19-2 the rest of the way, shutting out East Tennessee over the final 6:51 of the game, to pull away for the win.
"We really wanted to win this game," said Terrel Harris, who scored 15 points to join Anderson and Eaton in double figures. "We had that feeling way too much last year, losing at home by one or two points. We have grown up a little bit, as Coach Sean (Sutton) says. I believe this is a good win for us."
Sutton agrees with Harris.
"That was a good win and I'm really proud of my players for the way they competed down the stretch," said the Cowboy head coach. "We needed to be in a tight game like that with a good team.
"I thought the last seven or eight minutes we really fought and battled and showed some signs of getting tough. We shut them out the last seven minutes without a point. That's a great accomplishment. I'm proud of their effort and the fight they played with down the stretch," he added.
Anderson, who was 6-of-11 on three-pointers, has been on fire for the Cowboys. The freshman has now made 19 of 32 treys in his last five games.
"He's pretty hot," Sutton said. "One thing he did better tonight was take care of the ball. That's another thing with Byron, I was really pleased with was he didn't have a turnover in 24 minutes. I think the last three games he's had a total of two turnovers. He's doing a lot better job of protecting the basketball."
East Tennessee State Murry Bartow was certainly impressed with Anderson, saying, "I love Anderson. Anderson without question is going to be in the NBA. He's a great player, and we knew that coming in but he really hurt us," said Bartow.
Eaton only played seven minutes in the first half – and did not score a point – and had words for his coach when he was pulled from the game. But the second half was an entirely different story – 14 points, 3 rebounds, 2 steals, 1 assist in 17 minutes of play.
"I really challenged him at halftime," Sutton said. "In the first half he had nothing going for him. I told him at halftime this is a huge game and one that we have to win. You have to get out there and be a warrior, be the player that you can be and be tough on both ends.
"We're a lot better when he plays up to his capabilities. I thought he played well at both ends in the second half. He played with some fire and grit. He's a lot better player when he plays with that mindset," Sutton added.
The Cowboys made 13-of-32 three-pointers for 40.6 percent. The 13 made is the third most ever made in a game by an OSU team (the record is 15 set in 2004), and the 32 attempts is the second most alltime by the Cowboys (the record is 34 set earlier this season against North Texas).