A trademark header from Finnish striker Mixu Paatelainen and a thunderous free-kick from substitute Tom McManus were enough to give Hibs the edge over Aberdeen.
Paatelainen headed in a 70th-minute cross from John O'Neil and McManus buried Aberdeen with a 25-yard free-kick five minutes from time.
Aberdeen threatened first when Yannick Zamberdardi was caught out by a long through ball from Russell Anderson but Derek Young's angled shot was comfortably held by Tony Caig.
Young had another opportunity moments later but his shot from the edge of the box was tame and Caig collected easily.
Hibs came close in the 15th minute when Paco Luna managed to get his head to a John O'Neil cross but the ball drifted inches wide of David Preece's left-hand post.
O'Neil was also heavily involved when Hibs struck woodwork and came closest to breaking the deadlock in the 24th minute.
His free-kick was headed back across goal by Paatelainen for Derek Townsley but the midfielder's header struck the top of the crossbar.
Hibs held the upper hand at this point but too often their final ball into the Aberdeen penalty area was mediocre.
Eric Deloumeaux pulled a shot across the face of goal in a rare Aberdeen raid before Luna had a chance at the other end eight minutes from the break but directed a half-hearted effort at Preece.
Paatelainen came close to breaking the deadlock nine minutes into the second half when he connected with a cross from Jarkko Wiss but slid his six-yard shot wide.
Paatelainen missed a gilt-edged opportunity in the 62nd minute when Philip McGuire was cuaght in possession by Alen Orman in his own area. The ball broke to the Finnish striker who lofted it over Preece but wide of goal from 16 yards.
Chris Clark was equally careless at the other end shortly afterwards when Scott Michie set him up but he was wayward with his final shot as the Hibs defence opened up invitingly.
Paatelainen made amends for his earlier miss when he headed home an O'Neil cross at the back post. But Aberdeen almost equalised four minutes later when Caig misjudged a looping header from Laurent D'Jaffo and was grateful to see the ball strike the post.
But there was no way back for Steve Paterson's side when McManus curled in the second goal from a free-kick with five minutes left.