Alex Di Rocco had an acrobatic effort that sailed just over the bar in the first minute. Eoin Jess then weaved through the Killie defence to fire in a low shot, but Gordon Marshall was in fine form, diving low to pull off what was the first of a number of crucial saves.
Arild Stavrum nearly had the ball in the net in the ninth minute, but the Norwegian had strayed into an offside position.
Marshall made two more outstanding saves in the next ten minutes, one from a Winters curler, and the second from a Kevin McNaughton effort.
In the 37th minute, Kilmarnock made the breakthrough against the run of play. Andy McLaren capitalised after Aberdeen had needlessly lost possession in midfield to make it 1-0 to the visitors. Things went from bad to worse for the home team when, just one minute later James Fowler made it 2-0, again thanks to Aberdeen's lack of concentration in the middle of the park.
Aberdeen looked to get back quickly, and ARILD STAVRUM scored at the perfect time, just one minute before half-time. Darren Young crossed well, and the big Norwegian netted once again, from a suspiciously offside position, to bring his season's tally to five.
The second half started slowly, and with Gordon Marshall in top form the Dons were finding it hard to find a way through for the equaliser.
Stand in skipper Darren Young was forced to go off in the 56th minute with a hand injury, being replaced by brother Derek and eleven minutes later Phil McGuire was stretchered off with a shin problem, Jamie McAllister taking his place.
In the 80th minute, with Andreas Mayer on for Cato Guntveit, Stavrum had a great chance to level. He found himself one on one with ex-Celtic keeper Marshall, but the goalie once again made a magnificent save.
Aberdeen had a last minute chance when Di Rocco got on the end of a cross, but the on-loan Frenchman couldn't get the all important goal, his header being tipped over the bar for a corner by Marshall.
A thoroughly disappointed Ebbe Skovdahl offered no excuses after the match. "We created enough chances in the first half to win the match but couldn't convert our superioity into goals. There is a limit to the amount of points we can continue to drop, particularly at home."