Arkansas shot over 50 percent from the field for the second straight game, hitting 31 of 60 shots (.517) to offset a 27 of 35 performance by Tulsa at the free-throw line.
Gomez recorded the first double-double of his career with personal highs of 18 points and 12 rebounds. He kept Arkansas in the game in the first half, scoring 14 of UA's first 30 points as the Razorbacks rallied from a 21-12 deficit for a 38-38 halftime tie.
In the second period, Dean was six of nine from the floor, including three of three from three-point range. He finished with 18 points with 16 coming in the second half.
Dean's three-point play with 8:29 to play gave the Hogs a 61-59 lead.
After Charlie Davis gave TU (2-1) a 63-61 lead on a layup, Dean hit back-to-back treys from the left baseline and Jannero Pargo added a three to give Arkansas a 70-63 lead with 4:00 to play.
The Golden Hurricane cut the margin to 77-75 with nine seconds left on a free throw by Greg Harrington.
Satchell was fouled battling for the rebound on the missed second attempt and hit both free throws with eight seconds to go for the final margin.
Satchell was one of five from the line entering the game but was three of four against Tulsa.
Antonio Reed led Tulsa with 18 points.
Pargo had 13 points for the Hogs while J.J. Sullinger added nine points, two assists and a game-high four steals.
Arkansas plays host to Oklahoma Friday at 7 p.m. in a game televised nationally by ESPN2. The game was originally scheduled for Saturday at 6 p.m. but was moved for television.