The Swiss netted his fifth of the campaign after Killie captain Kirk Broadfoot was penalised for challenge on Jamie Maclaren.
The hosts had stormed into a two-goal lead after 23 minutes through efforts from Stevie Mallan and David Gray.
Kilmarnock, still aggrieved over the Scottish FA's decision not to overturn captain Gary Dicker's red card against Hearts, hauled themselves level before the break with strikes from Eamonn Brophy and Greg Stewart.
The visitors were first to threaten after Hibs were caught napping at a corner. Stewart played a short pass to Chris Burke, who got past Daryl Horgan, but the former Rangers winger's curling left-footed strike from outside the box flew past the post.
Hibs came out on top in a gripping 5-3 victory over Killie last time these teams met at Easter Road and Neil Lennon's side were up and running again inside 12 minutes.
Martin Boyle was felled by Aaron Tshibola just outside the area and Mallan added to his tally of set-piece goals with a stunning effort that flew into the top left corner beyond Jamie MacDonald.
Killie regrouped and went close moments later when Stewart created room in the box – but the striker's shot hit the side-netting.
However, the Rugby Park's side hopes of forcing their way back into the game diminished in the 23rd minute when captain Gray bulleted a header into the net.
Mallan was the provider with a corner and the right-back made no mistake from 12 yards as he directed his effort into he corner.
Just like in April, there were goals aplenty and Steve Clarke's side reduced the arrears three minutes later. Stewart found Stephen O'Donnell and the Scotland international's square pass was turned in by Brophy at the front post.
There was still more drama to come before the half was over as the Ayrshire outfit levelled in the 43rd minute.
Burke found Stewart on the edge of the box and the on-loan Birmingham midfielder fired a powerful left-footed drive past Bogdan from 20 yards.
Hibernian winger Thomas Agyepong game on for Boyle on the break and the hosts came close to retaking the lead within seconds of the restart.
Mallan was allowed to run at the Kilmarnock rearguard and the midfielder unleashed a venomous shot that bounced just past the post.
On-loan Manchester City player Agyepong also had a shot blocked in the box after doing well to create space.
However, Hibs got their winner 12 minutes from time after Kamberi beat MacDonald from the penalty spot.