This victory was a vital boost for the home side, who had suffered back to back defeats aginat Maroons and KCCA FC.
With the Barifa Stadium providing the setting, the match began in a lively fashion with both teams eager to take the initiative.
Blacks Power's Micheal Siwu came close to breaking the deadlock with a freekick, but Arua Hill's goalkeeper, Richard Anyama, was alert to tip the ball over the bar.
Then Arua Hill's Rashid Toha also came close to scoring from a freekick, but his effort was saved by Blacks Power's Emmanuel Odongo.
The visitors had a chance to take the lead when Isaac Tumusiime fired a low shot at goal, but it narrowly missed the target.
Arua Hill took the lead in the 29th minute when Media met Toha's header from a well-delivered corner kick by Gaddafi Wahab and guided the ball into the back of the net.
The Leopards doubled their lead in the 58th minute again through Media who showed pace and precision to grab his second goal of the game.
He received a through ball from Innocent Maduka, outpaced the goalkeeper and defender, and calmly slotted the ball into the empty net.
Blacks Power tried to find a way back into the match but failed to break through Arua Hill's defense.
Arua Hill thought they had scored their third goal through Maduka, but it was ruled out, while Toha missed another chance from a freekick.
The win moves Arua Hill to fifth place in the league standings, with 26 points from 17 matches.
Blacks Power, on the other hand, remain in 14th place with 15 points from 19 matches.
Arua Hill will next take on UPDF at Bombo Barracks Ground on Tuesday, April 4th, while Blacks Power will host KCCA on Wednesday, April 5th.