Leaders Hamilton Academical failed to keep up their blistering start to the new season, with the newly promoted side being held to a 0-0 draw at home by Kilmarnock.
And Inverness made the most of that slip-up, despite a late scare at Tulloch Caledonian Stadium.
John Hughes' side were made to work for the three points, with visitors St Johnstone putting in a disciplined defensive performance that took them into the break at 0-0.
But Marley Watkins provided the breakthrough with an hour gone as he slotted home after a fine one-two with Aaron Doran. Ryan Christie then doubled the lead five minutes later with a left-footed effort from inside the box.
The hosts might have hoped to cruise home as the final whistle approached, but Brian Graham's header ensured a nervy end to the game.
However, Inverness held on to leapfrog Hamilton, whose stalemate at home saw them drop to second place.
Elsewhere in the Scottish Premiership, Ross County's miserable start was extended as they were thrashed 3-0 by Aberdeen away from home to make it seven defeats from as many games.
Adam Rooney and David Goodwillie got on the scoresheet in the first half before Peter Pawlett netted a third in the second period in a comfortable win for the hosts, who move up to seventh.