Sodje rifled home a Matt Thornhill pass after Dons midfielder Peter Pawlett had been caught in possession, despite the home side having seemed the more threatening.
But the game quickly degenerated into end-of-season fare, and in the end the single goal proved to be the winner.
Dons defenders Zander Diamond and Rory McArdle joined a lengthy injury list in the 3-2 loss at St Mirren last time out, and they were among four changes made by the home side as manager Craig Brown looks to end a slump that has seen his side win just one of their past seven.
Nikola Vujadinovic and Ryan Jack came into the starting line-up, while Michael Paton and Josh Magennis dropped to the bench to be replaced by Sone Aluko and Nick Blackman.
Hibs also made four changes. On-loan Celtic man Richie Towell returned in place of Michael Hart after being ineligible for the midweek defeat at his parent club.
Derek Riordan was absent from the squad, while Martin Scott and David Wotherspoon joined Hart on the bench. Thornhill, Lewis Stevenson and Akpo Sodje came into the starting XI.
The Aberdeen players were looking to make their mark ahead of next week's Scottish Cup semi-final and they started the brighter of the two sides, particularly attacking down the right.
Peter Pawlett saw an early opening sliced wide after an Aluko pass had come back off Hibs captain Paul Hanlon, and he was later denied by the same player, this time from Chris Maguire's cross.
Aluko had seen Hibs goalkeeper Mark Brown hold a speculative 25-yard drive in between times, with the Dons looking lively.
Typically, though, it was Colin Calderwood's side who took the lead after 15 minutes.
Pawlett was caught in possession on the edge of his own box, and Thornhill's through ball was despatched confidently by Sodje.
Midway through the half, Maguire was unlucky not to level as he made space on the edge of the box, his low shot crashing back off the upright.
The game entered a bit of a lull, but with eight minutes remaining before the interval, a Derek Young cross found Blackman. The on-loan Blackburn Rovers striker, though, failed to get any purchase on his header.
Hibs should have given themselves some breathing space just two minutes after the restart as Ricardo Vaz Te slipped in Sodje, only for the first-half goalscorer to blaze high and wide.
The visitors failed to take advantage of a numerical advantage gifted to them by Vujadinovic's absence for treatment to a head knock suffered in a challenge with Sodje.
However both sides made changes before the hour and there was an immediate rise in tempo.
Hibs brought Wotherspoon and Colin Nish on for Sodje and Vaz Te, while the Dons replaced Blackman with Scott Vernon.
Seconds later, Maguire struck the upright for a second time, and from the rebound Aluko saw his strike turned wide by Brown.
Hibs countered, and after Wotherspoon had played him in, Stevenson forced Langfield into his first save of the afternoon, the keeper quick off his line to block from the midfielder.
Vernon volleyed wide of the far post from a Maguire cross midway through the first half, and two minutes later another delivery from the same man saw Aluko poke wide from a similar position.
Nish became the first to receive a yellow card after 72 minutes after catching Dons substitute Clark Robertson with a high boot, and he was followed into the book by Smith with five minutes remaining.
Smith had been switched to right-back when Robertson replaced Young, but the on-loan Norwich man's biggest impact was in attack as he cut onto his left foot, but sent his drive fizzing over.
The home side kept pushing into injury time, and Magennis was unlucky to see a header come back off the bar, before heading wide moments later.