Following their 2-1 Champions League defeat by Benfica in Lisbon in midweek Hoops boss Neil Lennon had claimed fatigue was impacting on his squad and it looked that way as they never got going against the neat and tidy visitors.
Kris Commons and Mikael Lustig missed good chances for the home side in an otherwise dull first half but there was no second-half surge from the champions and indeed, after McKay notched in the 65th minute from close range, he later spurned a good chance to double their lead when he hit the bar with only Fraser Forster to beat.
Aberdeen moved into second place thanks to a 1-0 away victory over Hibernian.
Niall McGinn struck 14 minutes from time to give the visitors the spoils as they moved level on points with Hibs, with both clubs just a solitary point behind leaders Celtic.
Dundee United came from behind to snatch the points with a 2-1 victory over Ross County in an action-packed second half at Global Energy Stadium.
After a goalless first half Iain Vigurs gave County the lead in the 48th minute with a glancing header.
Johnny Russell equalised within four minutes after he beat County goalkeeper Michael Fraser to a long ball on the edge of the 18-yard box - and United grabbed the winner in the 65th minute when Stuart Armstrong nodded in a Jon Daly knockdown.
Steven Thompson grabbed a double as St Mirren ended a poor run of results with a 3-1 win over bottom side Dundee in Paisley.
Thompson struck either side of a Ryan Conroy penalty, before Dougie Imrie put the gloss on the win with his first goal for the club against 10-man Dundee.
The victory ended a run of six straight defeats in the SPL for Saints.
Rowan Vine struck two minutes from time to hand St Johnstone a 2-1 victory over Kilmarnock in what was a bad-tempered clash at Rugby Park.
Home captain Manuel Pascali was controversially sent-off after four minutes, for a two-footed challenge on Nigel Hasselbaink.
Murray Davidson slotted the away side ahead on the half-hour mark, however the hosts battled back and grabbed a deserved equaliser seven minutes from the end when Michael Nelson headed home from James Dayton's free-kick.
The game looked set for a stalemate but Vine fired home on 88 minutes to clinch all three points for Steve Lomas' side.