The win is the 16th straight at home for the Razorbacks (2-0), who were 9-0 at home last season in the Southeastern Conference.
Harris scored 15 of his points in the first half for Arkansas, which trailed by as many as nine points early in the game. Qualls scored 12 in the second half, and the sophomore added eight rebounds and five assists.
Bobby Portis added 14 points for the Razorbacks, who were 27 of 53 (50.9 percent) from the field.
Elfrid Payton led the Ragin' Cajuns (2-1) with 27 points, while Shawn Long finished with 12.
Arkansas trailed 60-59 late in the game, but it answered with an 8-0 run in the closing minutes to take control and finally hold off what had been a difficult challenge from Payton and Louisiana-Lafayette.
The run included a jumper in the lane by Harris and four points from Qualls. Also, the Ragin' Cajuns struggled to hold on to the ball during the run - with a pair of turnovers leading to points for the Razorbacks and Payton being called for two charges.
Ky Madden's free throw capped a 17-3 closing run for Arkansas, which was 13 of 25 (52 percent) from the field in the second half.
After trailing for much of the first half, Arkansas went up 45-40 after back-to-back baskets by Anthlon Bell early in the second.
However, Louisiana-Lafayette used an 8-0 run to take a 53-48 lead, capped by an inside basket by Elridge Moore.
The Ragin' Cajuns led 60-59 after a putback by Long, but the Razorbacks took control from there.
Led by Harris, Arkansas' bench outscored Louisiana-Lafayette 32-11. The Razorbacks scored 19 points off 20 turnovers by the Ragin' Cajuns, and Payton - who was 9 of 18 from the field - finished with nine turnovers.
The two teams combined to finish 4 of 30 on 3-point attempts.
Sparked by Payton's fast start, Louisiana-Lafayette controlled the game early - jumping to a 21-12 lead after Hayward Register's 3-pointer.
Payton, a preseason All-Sun Belt Conference first team selection, scored the first four points of the game and finished with 16 points in the first half. The junior's quickness off the dribble proved difficult for Arkansas to cover early on, and he was 6-of-9 shooting in the half.
The Razorbacks rallied behind Harris, the junior transfer who sat out last season after returning to his home state following two seasons at Houston.
Harris had 15 points in Arkansas' season-opening win over Southern Illinois-Edwardsville, a number he equaled in the first half off the bench against the Ragin' Cajuns on 5-of-6 shooting.
His inside basket and following 3-pointer started an 11-2 run for the Razorbacks, who tied the game at 25 on a two-handed alley-oop dunk by Portis.
Louisiana-Lafayette went back up 33-29 after another inside basket by Payton, but Arkansas rallied to go back up 35-33 following a drive and one-handed dunk by Harris. Jacorey Williams' basket put the Razorbacks up 39-38 at halftime.
After hitting 8 of 16 3-pointers in its first game, Arkansas was just 1 of 9 from behind the arc in the first half on Friday. It finished 2 of 13 on 3-point attempts, while the Ragin' Cajuns were 2 of 17.
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