Gary Warren scored the decisive goal three minutes before the break at McDiarmid Park to settle a lively encounter.
The breakthrough came when Warren climbed above the St Johnstone defenders to head home from close-range after Richie Foran flicked on a David Raven centre.
In a lively opening in Perth Warren should have given the visitors the lead with an early header before St Johnstone stopper Alan Mannus made a good save the keep out a Billy McKay shot.
At the other end Stevie May drifted into space inside the penalty area but could only head the ball straight at Dean Brill from a David Wotherspoon cross.
And the Caley Thistle keeper produced an even better save as he got across to turn away a curling shot from Nigel Hasselbaink after the striker swivelled and dispatched an excellent effort.
May then combined with Hasselbaink but this time the Dutchman shot straight at Brill from inside the box.
Saints missed a glorious chance to level when Brill saved a drive from Wotherspoon and with the keeper on the deck Hasselbaink nodded the rebound wide from three yards.
Brill was again called into action to deal with a May drive from 30 yards as St Johnstone pushed for an equaliser but they could not make the breakthrough.