The loss was the Accies' first in three games but stretched their winless run to 12 games as they remain rooted to the foot of the table.
Impressive teenager Stevie May netted a double for his first league goals of the season for St Johnstone who are now equal on points with fifth-placed Inverness.
May powered from eight yards in just the fourth minute after being found by Collin Samuel who made a nice run down the right before doubling the advantage early in the second half with a deft flick over Accies gloveman Tomas Cerny after Alan Maybury's shot deflected into his path.
It was a superb performance by the 18-year old who was enjoying just his second start in Scotland's top flight and was not lost on Saints boss Derek McInnes who praised the 'natural' goalscorer.
"He's always been a confident boy. That's what I like about him, he's confident but is still a good lad. He's refreshing, he's come in at the right time and given us something," he said.
"He did well on his starting debut against Motherwell last week and there are certain games, against certain opposition, where we think he'll do well.
"He's got a real natural way of finding space and a natural movement about him that he always seems to get chances.
"He's done it since I first saw him at 14 and we always feel that something is going to happen and that's refreshing.
"He did well, he got the goals and he played his part, but I must stress he was part of a very solid and decent performance, and for that we're really pleased."