Issac Osbourne and Jonny Hayes provided the goals but the score does not come close to describing the visitors' superiority, particularly in a second half where Aberdeen controlled the play in the St Johnstone half and created numerous chances.
Nigel Hasselbaink added a late consolation for the hosts, but the defeat from the season home opener leaves St Johnstone with only a point from their first three SPL games.
Before kick-off St Johnstone boss Steve Lomas was dealt a blow as illness prevented Craig Beattie from making his debut.
Instead, Lomas went for Sean Higgins through the centre in a three-man attack that featured Hasselbaink and Liam Craig cutting in from either wing. Gregory Tade and Rowan Vine missed out through suspension.
An injury to Niall McGinn forced Aberdeen manager Craig Brown into a similar line-up reshuffle. Ryan Fraser came in and started on the left of a three-man attack with Scott Vernon through the middle and Jonny Hayes on the right.
Aberdeen started the brighter of the two sides with Fraser's direct running giving the visitors an early spark, and it was through the youngster that Aberdeen were able to open the scoring on 15 minutes.
Fraser's cross from the left was flicked on by Scott Vernon and dropped nicely for Isaac Osbourne arriving into the box. The makeshift right-back controlled the ball with one touch before smashing it low into the corner for Aberdeen's first league goal of the season.
The young attacker was at it again five minutes later after being played through on the left by a clever reverse pass from Vernon. The ball was passed across the face of the goal but Fraser Wright was able to clear before it reached the feet of the arriving Ryan Jack.
The hosts had looked disjointed in attack throughout most of the first half and Lomas reacted to this by withdrawing Murray Davidson and replacing him with Gary Miller, with the team reverting to a 4-4-2.
Within two minutes of the restart the change almost had an immediate effect, but Higgins fluffed a glorious chance when Craig's free-kick was deflected into his path six yards out.
Any momentum that could have been taken from carving out such an opportunity was gone 20 seconds later when a calamitous error gifted Aberdeen a two-goal lead.
There appeared to be little danger when a through ball for Jonny Hayes was comfortably covered by Fraser Wright.
However, the defender elected against putting the ball into the stands and waited for the oncoming Alan Mannus to clear. The indecision allowed Hayes to nick the ball from the pair and roll it into the empty net.
On 57 minutes Scott Vernon wheeled away in celebration having seemingly put his side 3-0 up with a bullet header inside the area, but his jubilation was cut short by the raised flag of the far side linesman.
The visitors felt aggrieved again after an initial Hayes shot rebounded off the post and back to Vernon in the penalty area.
His first time shot evaded Mannus but was deflected beside the post by one of the covering defenders. Aberdeen were incensed, feeling the deflection came via an arm.
The linesman's flag then denied Vernon and Aberdeen once again. The striker could not miss after running on to the end of a Fraser free-kick, but he was adjudged to have started his run too early.
Hasselbaink pulled a goal back late on after side-footing home from 10 yards, but the game should have been over as a contest long before this consolation, and the visitors were able to ride the nervy finish for a thoroughly deserved three points.