The Tigers used a 10-0 run in the second half to spark the victory along with a career-high 17 rebounds from junior center Peyton Davis plus 15 points from junior guard Tyrese Tanner, who made a key play by drawing an offensive foul in the final minute.
Arkansas had a final shot with a chance to tie, but the trey was off target.
The Tigers improved their record to 12-2 with their ninth consecutive victory. Arkansas fell to 12-2.
"It was a defensive game," Williams-Flournoy said, noting the Tigers trailed 20-19 at the halftime. "Arkansas is a very good defensive team. They were going to press and attack us. When two teams are pressing it usually isn't a pretty game."
The victory was the first for Auburn's new head coach vs. a ranked team in her short tenure with the Tigers. She noted that she told her players that their hard work in the offseason and pre-conference play showed on Thursday night. "This is where we want to be right now," Williams-Flournoy said.
Neither team shot well. Auburn was 21-64 (32.8 percent) from the field and hit 1-5 threes plus 7-11 free throws. Arkansas hit 16-58 field goals (27.6 percent) and 2-9 threes along with 9-10 free throws.
Auburn out-rebounded the Razorbacks 46-40 and had 16 turnovers, four fewer than the visitors.
The Tigers dominated the inside scoring 36-10 for points in paint and AU enjoyed an 8-0 edge in fastbreak points.
Hasina Muhammad added 13 points for the Tigers and freshman center Tra'cee Tanner came off the bench to contribute eight points.
Arkansas coach Tom Collin said he was impressed with the Tigers. "I give them credit," he said. "They are a pretty good basketball team. I hope this win over us gets them noticed. I look at them, and I know it's too early to say this, but I think they're a NCAA-type of team. I think if they play as hard as what they played against us tonight, they're going to win enough games to probably find themselves back in that hunt."
Asked if the Tigers passed the test in their first SEC game, Williams-Flournoy said, "They kind of did because you see the press working against a lot of our nonconference opponents, and you think it's good. We're forcing turnovers, but now will it work against a team that's really good? It should because nothing changes.
"As we go on people are going to have better press offenses. A lot of people are going to throw that long skip pass and make Blanche (Alverson) and Peyton (Davis) play a little bit better on the back line, but we'll switch up and go to another defense, and it will be fine."
Auburn returns to action on Sunday with a road game vs. Missouri.