Callum Davidson's men will now face Livingston or St Mirren - who meet at the National Stadium on Sunday - in the final at the end of February.
Hibs missed some good chances before captain Jason Kerr headed Saints in front from a David Wotherspoon corner 10 minutes before half-time.
Shaun Rooney scored with a superb header early in the second half and Craig Conway wrapped things up with a close-range finish in 63 minutes.
St Johnstone are aiming to lift the trophy for the first time, having been runners-up to Celtic in 1969/70 and Rangers in 1998/99.
.png){kind=logo}
