The Highlanders had gone five games without scoring before Mckay struck from point-blank range to give the hosts their first league triumph on home soil since overcoming St Johnstone 1-0 at the end of November.
Partick were left to rue not making the most of their first-half chances with Caley goalkeeper Dean Brill saving well from on-loan Sheffield United striker Lyle Taylor on three occasions.
Ross Draper had the first effort of the afternoon, testing Paul Gallacher with a low shot from 18 yards that the Partick goalkeeper comfortably held before Taylor could only fire an effort straight at Brill when given a clear sight of goal at the other end.
The visitors then had Kallum Higginbotham booked for diving after he went rather softly to ground in a challenge with Richie Foran.
Partick were steadily beginning to pose more of an attacking threat with both Higginbotham and Taylor trying their luck from outside the box but neither effort caused any real trouble for Brill.
The visitors continued to create the better chances as the half-hour mark approached, Taylor once more cutting in from the left before unleashing a strike from 18 yards that Brill did superbly to palm away diving to his right.
Brill foiled Taylor again shortly after before Josh Meekings made a fine block to deny Kris Doolan from slotting home the follow up.
Caley had been on the back foot for much of the first half but a moment of inspiration almost saw them take the lead against the run of play.
The ball bounced up nicely for Greg Tansey 25 yards out, who elected to try his luck with an audacious half-volley that only just went wide of the upright.
The midfielder had an even better opportunity, however, in the opening exchanges of the second half. Mckay's flick on put Tansey in on goal, but his attempted lob over the onrushing Gallacher landed on the roof of the net.
It was now the home side's turn to enjoy the better of the play in the final third and Mckay will feel he should have done better than fire wide from 12 yards when played in by the impressive Tansey.
The hosts, however, were almost caught out when Higginbotham set up Taylor but the offside flag was up well in advance of the striker slipping the ball beyond Brill.
Play surged straight to the other end and finally Caley made the breakthrough. Draper's header across goal made it all the way to the back post to where Mckay was lurking and he made up for his earlier miss with a simple finish (62) much to the delight of the home fans.