The visitors were forced to play almost half of the Rugby Park contest with 10 men after David Raven brought down Josh Magennis in Caley Thistle’s penalty area two minutes after the interval.
Alexei Eremenko slotted home from the spot and Magennis soon missed a sitter to double the lead as the home side failed to make their numerical advantage count.
McKay levelled in the 54th minute following some great individual skill and converted another impressive goal in an 82nd-minute counter-attack to send the Highlanders into the top three.
Northern Ireland forward McKay had had a couple of early openings as the visitors began strongly in the Ayrshire snow and sleet, firstly seeing a shot well-blocked by Mark Connolly and a glancing header saved by Craig Samson.
Eremenko was then just over with two efforts for the home side, the first taking a deflection off the head of Thistle
defender Josh Meekings, and Lee Miller volleying an ambitious shot not far wide.
The wind and snow eased just as an unexpectedly open second half began and the catalyst to some improved entertainment was Rory McKenzie’s astute through-ball. It caught the visiting defence flat-footed with Magennis running on to it and going down under the sliding challenge of Raven, who was already walking towards the tunnel when referee Don Robertson flashed his red card. The right-back had been booked for a wild tackle on Craig Slater but there was no second yellow anyway.
Eremenko took the ball off Magennis before slotting the penalty just inside Dean Brill’s right-hand post, despite the goalkeeper getting a good hand to it.
Magennis soon missed a glorious chance to put the game beyond the 10 men after McKenzie collected a short corner and worked space to drive the ball across goal. Brill could only palm it up into the path of Magennis but the former
Aberdeen man headed over from six yards with the goalkeeper grounded.
McKay made him and Killie pay dearly by latching on to Graeme Shinnie’s ball down the right channel and flicking it over the head of a home defender before controlling and coolly slotting home the equaliser with his left foot.
Eremenko’s misplaced back header then sent McKay clear from the centre circle but Lee Ashcroft caught up with the forward and forced him off the ball as Thistle threatened a second.
Killie keeper Samson tipped over a thundering 25-yard strike from Greg Tansey before the visitors snatched all three points. McKay picked up the ball just inside the home half and ran forward before playing a one-two with Nick Ross and sweeping the ball into the corner of the net from 18 yards.