Goals by Chris Burke, Egil Ostenstad and Michael Mols at Ibrox were enough to send Alex McLeish's (pictured) side to the final four stage, as The Saints had no reply to the Scottish Treble winners in the end.
The Gers will be joined in the semi-finals by cash-strapped Dundee, who needed extra time to defeat Hearts 1-0 at Dens Park.
Both sides were unable to break the deadlock in normal time and it was not until the 107th minute that The Dark Blues found a breakthrough.
Robert Linn was Dundee's hero on the night, as the result will give the Tayside outfit a chance to earn some much-needed cash with a semi-final encounter to come.
Click below for match summaries:
CIS Insurance Cup
Dundee 1-0 Hearts (AET)
Rangers 3-0 St Johnstone
