Alabama responded by scoring the next 17 points, six by Rod Grizzard, to take a 38-20 lead with 3:24 to play in the period.
Arkansas cut the deficit to 39-26 on a Sullinger free throw, but the Tide went on an 11-4 run to take a 20-point lead before settling for a 52-34 advantage at the half.
Alabama led by as many as 35 in the second half, 92-57 with 9:03 to go, but hot shooting by Pargo, and season-best efforts from Blake Eddins and Larry Satchell helped the Hogs close within the final margin.
Pargo, who had a career-high 35 points in Saturday's 94-92 overtime victory over No. 4 Florida, had his second straight 30-point game and his fourth of the season with 33 against the Tide. He had 23 points in the second half and finished the game hitting nine of 19 shots, including seven of 14 three-pointers.
His last bucket, a trey with 2:23 left, got UA within 107-83. Eddins scored seven of his season-high 11 points in a 34-second span to cut the margin to 107-91 with 59 seconds left. Satchell had five of his season-high matching eight points in the final nine minutes.
Other than Pargo, the bright spots for Arkansas were freshmen Sullinger and Michael Jones. Sullinger had 11 points, three rebounds and three assists while Jones had his first double-double with career highs of 18 points and 10 rebounds.
Grizzard and Earnest Shelton led Alabama with 21 points each.
Both teams shot 60 percent in the second half and the Hogs were even on the boards, 39-39, but Alabama made 18 of 39 shots in the first half (.462) while the Hogs were just 11 of 34 (.324). Arkansas also forced just four first-half turnovers while losing the ball 10 times. For the game, UA had 15 turnovers and Alabama 13.
Arkansas plays host to Auburn Saturday at noon in a game televised by Jefferson-Pilot Sports.