Reed hit 7-12 field goals, including 4-7 threes, as he led all scorers with 20 points. He also contributed four assists and two steals.
Barber scored 15 points and was Auburn's leading rebounder with 10. It was his fourth double-double in the last five games.
As a team the Tigers won the rebounding battle 40-36 and held a huge edge in free throw shooting. The Tigers made 20-28 free throws for 71.4 percent while the Green Wave made just 10-22 at the foul line.
"We did a good job the last two games making some free throws," Auburn coach Jeff Lebo said. "I won't talk about it too much. As soon as I do, something disastrous will happen, but the last two games they have done a good job of putting the ball in the bucket.
"We got to the line so much in the first half--we got 21 free throws," noted Lebo, whose team lead 40-27 at halftime.
The coach noted that Barber, who had four offensive rebounds, and Lucas Hargrove with five of his eight boards being offensive rebounds, continue to work hard on grabbing missed shots. Hargrove finished the game with nine points, three assists and a steal.
The Tigers got 11 points off the bench from Rasheem Barrett, who chipped in with three rebounds, two assists and two steals. The senior also won praise from Lebo with how he attacked the defense with his drives into the lane.
Quantez Robertson continues to show signs of coming out of his shooting slump. He was 2-4 from the field, including 1-2 on threes, and made 4-6 foul shots.
Former Auburn High star Asim McQueen a 6-7, 240 junior forward, led the Green Wave in scoring with 16 points. He added four rebounds and three assists much to the delight of his friends and family in the crowd of 4,870 at Beard-Eaves Memorial Coliseum.
"I had a pretty good individual game, but I would have rather had a win," McQueen said.
Auburn's Tay Waller shoots over Asim McQueen on Saturday night.
Kevin Sims, a junior guard, added 14 points for Tulane, which fell to 6-7 with the loss.
Auburn improved to 10-4 with the win as the Tigers head into SEC play next Saturday at South Carolina. Barber said the winning streak is nice, but added that his Tigers should have won more games.
"We have a lot of confidence going into conference play," Barber said. "We needed those seven games in a row.
"The way I feel, we should be undefeated," the senior added. "We gave away few games. A few of the games we lost at the free throw line. We lost against some very good teams. A seven-game win streak is real good going into conference. Hopefully, we will continue to win more games off this little momentum."
The seven-game streak is the longest of the Lebo Era at Auburn and matches the longest since the 2003-2004 team under Cliff Ellis won its first seven games of the season.
Lebo said defense, as has been the case in recent weeks, was the key to victory for the Tigers, who held the Green Wave to 37.3 percent shooting.
"I thought we did a nice job defending," the coach said. "We spent a lot of time the last two days defending all of their stuff and for the most part we did a very good job.
"On their post guys, McQueen hurt us a little bit when we stopped doubling. He played very well, but other than that I thought we did a nice job overall."
The only thing he didn't like was the Green Wave getting out to a 10-0 lead, but he even saw a silver lining to that dark cloud. "I liked the way when they punched us in the mouth we didn't panic," Lebo said. "We just stayed the course."
Reed agreed with Lebo that the Tigers are winning games with defense after allowing the Green Wave just 53 points.
"We are doing a good job on the defensive end and have been," the junior guard said. "We are helping in the post. We are doing a good job of getting everybody to talk on defense and getting everybody in the right spots."
Reed also led the Tigers with 20 points in their last game vs. Southeastern Louisiana. "He seems to be playing with a lot of confidence," Lebo said. "The one thing with DeWayne in everything he does is that he needs to feel comfortable and he finally feels comfortable and is more consistent, which is what I like to see from the upper classmen."
The Tigers used 11 players, with eight seeing significant action. "I thought our depth was a factor in the game," Lebo said. "At the end their two big guys looked a little fatigued."
The Tigers fell into a quick 10-0 hole before breaking the ice with a fastbreak basket by Frankie Sullivan at the 16:54 mark. He finished the game with seven points.
The Tigers pulled even at 10:19 mark as a stuff by Barber on which he was followed resulted in a three-point play as the senior made the foul shot to tie the game at 17-17.
The Tigers took the lead at 24-22 on a steal and dunk by Tay Waller with 7:17 left in the first half. Two free throws by Waller with 4:38 built the lead to 30-22. Waller finished the game with seven points.
Tulane cut Auburn's lead to 48-43 at the 15:24 mark of the second half, but the Tigers scored nine uncontested points and steadily pulled away for a 25-point margin of victory.
Tulane coach Dave Dickerson said he was proud of his team's effort against an Auburn team he said is playing well. "Auburn is a very solid team--definitely the most athletic team we have played all year," he said. "Whenever DeWayne Reed is hitting shots like he was tonight, it makes it tough to play good defense."
Lebo said the Tigers will have their hands full on the road vs. South Carolina, a team that pulled off a road victory at nationally-ranked Baylor. "Anytime you go on the road in the SEC, it isn't easy," Lebo said.
The game at Beard-Eaves Memorial Coliseum was the second half of a doubleheader. The ninth-ranked Auburn women's team improved its record to 15-0 with a 79-55 victory over Stephen F. Austin.