Auburn led 46-42 at halftime, but the Tigers were outshot from the field 50 percent to 38.7 percent in the second half to pull out the victory.
Auburn fell to 2-5 while DePaul improved its record to 4-3.
"It's frustrating, but we did a lot of good things," Sullivan said. "We have got to find a way in the last four minutes to win a game."
Senior guard Noel Johnson's three-pointer from the top of circle tied the game at 72-72 with 2:33 to play, but the Tigers struggled to score down the stretch.
Auburn still had a chance to tie the game or win in the closing seconds trailing 78-76, but a turnover prevented that from happening.
"We're getting closer--we just have to put it all together at one time on the floor," Coach Tony Barbee said. "The other night we had our younger guys play well on the floor and our veteran guys not play so well.
"Tonight I thought our veteran guys did what we needed them to do--carry us in big moments--and our younger guys didn't quite have the games they had the other night."
The coach said the Tigers had their best week of practice with more energy and that "turned into a better performance for us because of that."
However, Barbee added, "Obviously, there are some clear things we have got to work on."
The Tigers got a career-high 28 points from senior guard Frankie Sullivan, who added five assists and four rebounds. Sullivan hit 9-17 field goals and was 4-7 on threes and 6-6 at the foul line. He split his time between playing point guard and two guard.
Senior center Rob Chubb scored 17 points and pulled in 13 rebounds for the Tigers.
Rob Chubb shoots for the Tigers.
Melvin Cleveland led the Blue Demons with 21 points and 10 rebounds.
Auburn finished the night shooting 43.8 percent from the field as it hit 28-64 field goals.
DePaul made 26-54 field goals, but nailed 9-17 treys. Auburn made 6-16 three pointers.
Auburn won the rebounding battle 43-32 and turned the ball over 14 times, one more than the visitors.
The Tigers hit 14-21 free throws while DePaul made 19-34 foul shots in a game the visitors got an unusual number of unusually friendly calls from the officiating crew of Joe Lindsay, Roger Ayers and Ed Corbett.
"We have a lot of young guys and they are starting to realize it is a struggle," Chubb said. "It doesn't come easy. It's not handed to you. It's something that you have to take. The thing is they are starting to get it.
"We're getting close," Chubb added. "We're starting to come together as a team."
Suspended: Juco transfer forward Shareif Adamu did not play and is suspended indefinitely for a violation of team rules, Barbee said.
Halftime Numbers: Auburn made 16-33 field goals for 48.5 percent in the first 20 minutes while DePaul made 14-30 for 46.7 percent. Auburn hit 4-10 threes while DePaul made 6-10. Auburn was 10-14 at the foul line while DePaul made 8-16 free throws.
Auburn held a 24-15 rebounding edge at the break and turned the ball over nine times, one more than the Blue Demons.
Sullivan led the Tigers at the break with 20 points as he hit 6-9 field goals including 4-6 treys and 4-4 at the foul line.
DePaul's Coach: Oliver Purnell called his team's performance a "grind it out game." He noted he told his Blue Demons to expect a high energy performance from the Tigers and they got that on Friday night. "They were going to play with a lot of desperation and they're fine, fine athletes."
Up Next: The Tigers will be off until fall semester final exams are finished. Their next game is a home contest on Dec. 11th vs. Grambling. "It's miserable when you have to wait that long," Sullivan said.