Auburn outscored the Racers 19-2 in points off of turnovers and held a 41-31 rebounding advantage in a game the Tigers led except for several seconds early in the second half.
Denson hit 7-13 field goals and 9-15 free throws while the Tigers made 23-33 foul shots as a team.
Senior forward Allen Payne added 10 points and seven rebounds for the Tigers, who improved 3-1 while Murray State, a team that defeated Auburn by 20 points last year, dropped to 2-3.
Auburn coach Tony Barbee said his team's overall toughness was a factor in the victory, something that showed up in the stat sheet, particularly with Harrell pulling in 10 rebounds from the guard position.
"It was me just being aggressive defensively, and offensively, attacking the glass," Harrell said. "I have got to do that a lot more. I think that will help us win games."
Auburn's biggest lead was just 12 points with 4:47 to go. The Racers cut that in the half, but Auburn made the plays down the stretch to win the game, something they have had trouble doing in recent seasons.
"That just comes with the leadership on the team," Denson said. "I am not knocking all the people we have had here in the past. We have great leadership. We just have the team chemistry. If we didn't have team chemistry, we wouldn't have gotten those clutch stops we needed.
"Back then we would have probably gave this game away, but this year with the leadership and chemistry it was a good win tonight," Denson added.
Auburn led the entire first half, building the margin to nine points late in the period, but the Racers made a late run to cut the lead to 32-28 at intermission.
The Racers briefly took the lead with a pair of back-to-back threes, but the Tigers immediately answered and led the rest of the contest.
The Tigers also got a solid game from seven-foot center Asauhn Dixon-Tatum, who scored 10 points on just five field goals. He added six rebounds and three blocks.
Dixon-Tatum made four of his five shots vs. the Racers.
Freshman point guard Tajh Shamsid-Deen scored 11 points and added two assists with one turnover and one steal in 30 minutes of action.
"I am proud of all the guys the way the fought," Barbee said. "Murray State has a culture about itself and it is what we are trying to develop here. I was worried about this game.
"I talked to my team that this team, regardless of who is on it, it is going to fight. They are going to throw punches, not literally but figuratively. They are going to keep coming at you. I was proud of the way we sustained the runs they made and were able to bounce back and created something for ourselves.
"That is what we want to become," the Auburn coach added. "We want to become that tough-minded team that doesn't get rattled through anything."
Auburn shot 44.4 percent from the field while the Racers hit 45.5 percent. Auburn was 4-18 on threes (22.2 percent) while the Racers made 7-16 threes.
Worth Noting: Murray State head coach Steve Prohm said Auburn deserves credit for the win. "They were resilient and they made tough plays on the offensive glass late," he said. "They drove us in the zone."
Stat of the Game: Auburn pulled in 27 defensive rebounds and 14 offensive rebounds to finish plus 10 in that category. "The rebounding was big," Barbee said. "It was one of the things I highlighted on the board about this team. They take pride in their toughness and part of that shows up in their rebounding stats."
Halftime Numbers: Auburn hit 10-25 field goals (40 percent) in the first 20 minutes and made 2-10 threes and 10-15 field goals. The Tigers out-rebounded Murray State 23-13 in the half and committed seven turnovers, three more than the Racers. K.T. Harrell led the Tigers in scoring with nine points while Asauhn Dixon-Tatum added eight. Murray State was 11-27 from the field in the period and hit 1-6 threes and 5-11 free throws.
Auburn returns to action with a 7 p.m. home game on Tuesday vs. Tennessee State.