May went close for the visitors in the opening minutes of the game, but he saw his right-footed shot from the centre of the box saved in the bottom right corner.
Nadir Ciftci had United's first attempt as he let fly with a left-footed shot from outside the box. However, it wasn't enough to trouble the St Johnstone goalkeeper, who held firm.
Johnstone took the lead just after half time when May tried something special from distance, with his effort ending up in the back of the net.
The visitors could have put the game out of sight in the 60th minute, but Michael O'Halloran headed over the bar from the centre of the box.