With just over one minute on the clock, Celtic opened the scoring when Ki Sung-Yong delivered a low free kick back into the St Johnstone penalty area from wide on the right and Stokes fired in from 18 yards.
Stokes replied with a right-footed effort from the edge of the St Johnstone penalty area that Smith held well, then the Northern Ireland international missed with a close-range header from a Mark Wilson long-ball.