In an absorbing encounter, Sodje opened the scoring and Palsson added a second from the penalty spot.
The visitors then found the net from 12 yards through Jamie Hamill as Francis Dickoh was sent off for a professional foul.
Referee Steve Conroy then struggled to keep control in the dying stages when both benches and just about every player became involved in a melee.
The result sees Hibs move eight points clear of basement side Hamilton in the Clydesdale Bank Premier League.
In a lively start, on-loan Everton marksman Kieran Agard had a low left-footed shot from outside the area saved by Graham Stack after Dickoh gave the ball away following a timely tackle on Liam Kelly.
The pace of the visitors' attacks were causing Hibs problems and the home fans were relieved to see Agard slip another effort wide of the far post after being teed up in the box by Mehdi Taouil.
The tempo of the game calmed following a frenetic start, but Kilmarnock continued to enjoy the lions' share of possession.
Building from the back, the Ayrshire outfit were looking to pass their way through Hibs with Taouil and Rui Miguel offering support to Agard.
After 33 minutes, Hibs youngster Callum Booth was caught in possession at the corner flag as Agard continued to terrorise the home rearguard. The Toffees youngster then edged past Dickoh inside the area but slammed a left-footed shot into the side netting with only Stack to beat.
Hibs continued to look uneasy at the back and Stack pulled off a great save to push Taouil's stinging effort behind after the Leith outfit failed to clear the danger from a Garry Hay corner.
Kilmarnock were forced into a half-time change with goalkeeper Cammy Bell being replaced by Anssi Jaakkola.
The Finn was called into action minutes after his introduction when Riordan hit a free-kick straight at the goalkeeper.
Hibs then had penalty appeals waved away by referee Conroy after Sodje fell in the area under a challenge from Mohamadou Sissoko.
After spending most of the first half keeping Kilmarnock out, Hibs took the lead in the 53rd minute when Sodje opened his account for his new employers.
David Wotherspoon headed into the path of the former Charlton man, who raced away from Manuel Pascali after the Italian fell to the ground, and Sodje passed the ball beyond Jaakkola into the net via the inside of the post.
Pascali claimed he had been fouled by the goalscorer but his appeals fell on deaf ears.
Hibs doubled their lead in the 69th minute when January signing Palsson notched his first goal for the club from the penalty spot.
Riordan appeared to be caught in the face by the arm of Sissoko and former Liverpool midfielder Palsson sent Jaakkola the wrong way from 12 yards.
Kilmarnock reduced their arrears in the 74th minute courtesy of Hamill under controversial circumstances.
Dickoh brought down Agard in a last-man challenge inside the box, but it was near-side assistant referee Keith Sorbie that flagged for a foul.
After discussing the incident with his colleague, Conroy issued a red card to the Hibs defender and Hamill made no mistake form the penalty spot.
An ugly melee involving both benches and nearly every player on the pitch then left Conroy struggling to restore calm.
It all started when Hibs sub Martin Scott went into a crunching challenge with Tim Clancy in front of the dugout, prompting Kilmarnock manager Mixu Paatelainen to get involved.
When the action resumed Craig Bryson was denied a last-gasp equaliser after Stack made a superb block.
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