McKay struck twice in the first half to take his tally for the season to five goals and put Inverness in command at the interval, before the hosts went on to dominate after the break.
The Northern Ireland international could have had a treble when Hearts captain Jamie Hamill saw red for what referee John Beaton deemed to be a handball inside the area late on.
McKay was given the opportunity to claim his hat-trick ahead of regular penalty taker Vincent, but visiting goalkeeper Jamie MacDonald saved his effort.
Despite this, Caley Thistle manager Butcher was pleased to have overcome a spirited Hearts team.
He said: "Hearts might be bottom of the league, but on current form before the game they would have been sitting fourth.
"They are still formidable opponents and they certainly showed spirit and determination, but we had some great chances to have finished the game off.
"I was a bit concerned that there might be a sting in the tail, although I couldn't see it.
"The only slight disappointment was the penalty. I understand the sentimentality of it, to give Billy his hat-trick, but James Vincent is our penalty taker and he will be hitting the next one."
Hearts boss Gary Locke did not want to focus too much on the penalty incident and hoped instead the defeat would not be too damaging in the Jambos' bid for survival.
He said: I spoke to Jamie Hamill after the game and he said the ball hit him on the head, but when I spoke to the referee, he said it was handball.
"It's a difficult one, but I don't really want to make too much of it as I don't want to make any excuses.
"Inverness were really good and twice caught us in the first half on the counter attack.
"You are going to get these days. We've had a great few weeks where we've not really had many setbacks, so it's not the end of the world."