Jamie Hamill put the game beyond the Dons early in the second period on Saturday after Israeli referee Eli Hacmon ruled that Jamie Langfield had brought down Alexei Eremenko.
Aberdeen complained but there was little doubt about who the better team was following Conor Sammon's opening goal. Hacmon produced an assured performance after replacing striking Scottish officials and there appeared to be contact at the penalty incident despite complaints from the visitors.
Aberdeen have now taken just four points from a possible 39 and their second-half performance offered little encouragement they can turn their fortunes around in the near future.
Snow was cleared off the pitch before kick-off to allow Hacmon to take charge of his first Scottish game, assisted by compatriots Eyal Hatuca and Amihay-Yesoshhua Mozes with Malta's Marco Borg acting as fourth official.
Both teams made one enforced change after having players sent off last weekend. James Fowler replaced Mohamadou Sissoko for the hosts with Aberdeen's Yoann Folly coming in for Rory McArdle.
There was still a light dusting of snow in some areas and several players lost their footing in the opening moments. Both sides struggled to piece together any meaningful spells of possession, with even the normally impressive Eremenko wayward with a number of long-range passes.
Hacmon strolled through the initial stages without controversy and there was little dispute about the free-kick decision that led to Kilmarnock's 18th-minute opener.
Jerel Ifil slid in recklessly on Sammon to allow Eremenko an opportunity to shoot from 20 yards. The Finn's curling effort did not appear immediately threatening but Langfield spilled the ball and Sammon won the race to slide home the rebound and net his eighth goal in six games.
Killie experienced an initial lift before Aberdeen began to produce some sustained passing, but the only time Cammy Bell was troubled was when he had to punch away Sone Aluko's corner from underneath his crossbar.
Hacmon issued his first yellow card in the 37th minute for Andy Considine's poor challenge on Mehdi Taouil and even received some polite ripples of applause as he made his way off at half-time.
The referee's quiet afternoon was shattered four minutes after the break when he was faced with a difficult decision when Eremenko went down under Langfield's challenge in the box.
Aberdeen had been exposed at the back by Craig Bryson's pass into their half for Sammon to race on to. The Irishman played a composed square pass to Eremenko, who took the ball too wide as Langfield confronted him before going down.
Eremenko's fall was undoubtedly exaggerated but Langfield looked, from a distance, to have made contact and the Israeli pointed to the spot.
The Aberdeen goalkeeper remonstrated with Eremenko while some of his team-mates complained to the referee, before Jamie Hamill stepped up to send Langfield the wrong way.
Killie almost went further ahead after another slick break. Eremenko threaded the ball through for Sammon, who turned inside his man and drew an excellent save from Langfield, although the unmarked Taouil had wanted a pass from both men.
Eremenko then set up another chance with a brilliant pass inside the full-back with Langfield getting down to save from Liam Kelly following the cutback.
Hamill was booked for bad foul on Aluko as Aberdeen attacked, but the Dons looked a beaten team after the penalty.
Scott Vernon got several headers on target but Bell was never really troubled and Sammon almost capitalised again as Langfield initially mishandled Hamill's drive.
Killie kept the ball from a demoralised Aberdeen for long spells in the final stages, with Langfield producing another save from Eremenko.