Dunham entered the game averaging nearly 17 points per game, but missed 10 of his dozen shots en route to six points, which was his second-lowest total of the season. However, he pulled down nine rebounds, which topped his previous career-best of seven boards.
Barlow connected on 7 of his nine shots, including a buzzer-beater at halftime off a steal in the final seconds and totaled 19 points, three higher than his previous best offensive effort.
Butler senior Khyle Marshall added 18 in helping the Bulldogs (13-16, 3-14 BE) remain a half-game ahead of the Blue Demons (11-20, 3-15) in the league standings.
Barlow also sank a career-best four of five from 3-point range, and he added five steals, three assists and three rebounds. He had 13 points in the first half, while helping Butler to a 38-18 halftime lead.
Marshall split his points evenly in the first half and second half and he added four rebounds and a steal in 27 minutes of action.
The Bulldogs jumped to an 18-4 lead in the first 10 minutes of the game, and DePaul never got closer than 10 points the rest of the way. Butler opened the second half with a 15-2 run to increase the lead to 53-20 with just over 16 minutes remaining.
Two minutes into the second half, Barlow had 18 points and DePaul had 18 points.
Butler's 79-point outburst came just one game after the Bulldogs scored a season-low 48 points in a loss at Villanova. The 79 points were the Bulldogs' second-highest total in a regulation Big East game this season.
"We were efficient on the offensive end," Miller said. "We got the shots that we wanted and we got the ball in the paint."
Barlow scored eight of the 18 points in Butler's opening run. He went on to hit five of six shots in the first half, including all three of his three-point attempts.
"Alex is always one of our more solid guys, one of our sound guys," Marshall said. "He's definitely capable of scoring in double-digits as he's done throughout the season. He was hot tonight. Our guys did a good job of getting him the ball, and he did a good job of finding his spots. He played a very complete game tonight."
Miller used all 13 players on his roster, and 11 of those players cracked the scoring column. Butler's bench outscored DePaul 24-10.
Brandon Young, playing his final home game for DePaul, led the Blue Demons with 24 points, while freshman Billy Garrett added 12.
The Bulldogs finished with a commanding 46-29 rebounding advantage, including a 16-6 edge in offensive rebounds.
Butler can clinch the No. 9 seed for the upcoming Big East Tournament with a win in its final regular season game against Seton Hall on Saturday at Hinkle Fieldhouse (4:30 p.m., Fox Sports 1).