The scoreline was genuinely harsh on the Saints, who enjoyed the majority of the possession but were let down by slack defending as two goals from Jonny Hayes and one each from Peter Pawlett and Adam Rooney sent the Dons to Hampden.
Hayes fired Aberdeen into a third-minute lead when he slid in to convert a low cross from the right by Rooney, who had a free-kick tipped over by Steve Banks moments earlier.
But St Johnstone responded positively as Stevie May tested Jamie Langfield from distance, and Steven Anderson headed wide from Lee Croft's corner.
Frazer Wright then drilled over as Saints continued to pressure, and Croft got in behind the Dons defence only to be denied by a stunning save by Langfield.
St Johnstone fans may have sensed this was not to be their day when Aberdeen doubled their lead on 32 minutes against the run of play.
A cross from Hayes was only partially cleared, and Pawlett skipped past a static defence as he drove into the box before slotting a cool finish under Banks.
The agony continued for Saints after the break when Wright's header cannoned back off the woodwork and Anderson was unable to hook the rebound on target.
Banks dived bravely at the feet of Rooney as Aberdeen countered, but he was beaten again on 63 minutes when Rooney latched onto Pawlett's precision through-ball and curled beyond the advancing Saints keeper.
Hayes lashed wildly over the bar, and Andrew Considine almost added a fourth as his towering header beat Banks but crashed off the bar.
But as St Johnstone shoulders sagged, Hayes rounded off the scoring with 11 minutes remaining as he cut in from the left and belted an angled drive across Banks and into the far corner.