Inside 25 minutes, Rangers were three up and the game was over.
Hamza Igamane, Vaclav Cerny and Mohamed Diomande all capitalised on poor defending as Clement's men looked intent on blowing their opponents away.
An early goal was sought to ease tension and came from a common source. St Johnstone switched off at a throw-in, Cerny fed Diomande who cut back for Igamane and he made no mistake with his 12th goal of the campaign.
It was poor from Valakari's side and again so when Robin Propper won possession and Cerny scampered clear to finish past debutant Andy Fisher in goal.
A third came as St Johnstone looked likely to implode. Jack Sanders aimlessly headed straight to Diomande and he nodded the gift home.
At that stage it seemed a case of how many. To their credit, St Johnstone grew after changes at the break.
From their first effort on target, they scored. Max Kucheriavyi floated a delightful corner in and Sanders atoned for his earlier error by netting a consolation.
That sparked a little more threat and nervousness around Ibrox but was ultimately too little too late.
Substitute Oscar Cortes came closest to extending Rangers' lead with a curling shot that Fisher superbly diverted.