Pargo hit two free throws to cut the deficit to 58-55, but the Volunteers got two free throws each from Thaydeus Holden, Jenis Grindstaff and Jon Higgins to push the advantage to 64-58 with 56 seconds left.
Arkansas missed three layups, all in traffic, the rest of the way and never got closer than six.
The Razorbacks, playing their second game under interim head coach Mike Anderson following Saturday's 81-67 home victory over Vanderbilt, shot 50 percent in the first half (14-28) and led 35-31 at the break.
Vincent Yarbrough's free throws cut an eight-point deficit to 50-44, but Gipson made one of two free throws for the seven-point lead with 7:25 to go.
UA senior Brandon Dean finished with team highs of 16 points and six rebounds while Gipson had 12 points and four rebounds. Pargo finished with nine points, seven assists and three rebounds while Alonzo Lane had eight points and five boards.
Yarbrough led Tennessee with 20 points and 14 rebounds. Marcus Haislip had 12 points, Brandon Crump 11 and Jon Higgins 10.
Arkansas forced 14 turnovers and got just nine points off the miscues while UT had a 43-30 rebounding edge and outscored the Hogs 22-15 at the line.