Maguire broke the deadlock after four minutes when he turned home a Paul Hartley corner from close range and Vernon netted a second for the Dons with a neat finish just before the break.
St Mirren pulled a goal back through a Nikola Vujadinovic own goal in the closing stages, but the Dons held on for victory and will take on Celtic at Hampden next month.
Northern Irishman Rory McArdle, who scored deep in injury-time to earn the Dons a 1-1 draw in Paisley and salvage a replay, tonight started in place of the injured David McNamee.
Midfielders Sone Aluko and Ryan Jack were also named in the starting XI with Vujadinovic and Josh Magennis dropping to the bench.
The visitors only made one change, with former Falkirk striker Michael Higdon preferred to Jim Goodwin who started on the bench.
Aberdeen, who had only scored three goals in their previous five games, should have gone in front when Maguire's low drive across goal was turned against the bar by the sliding Aluko and cleared for a corner.
However from the resulting set-piece the Dons went ahead when Zander Diamond flicked on Hartley's inswinging corner for Maguire to bundle the ball home from close range.
St Mirren had a great chance to pull level when Paul McGowan's cross into the box was headed clear by Diamond only as far as Steven Thomson but the midfielder sliced his shot wide of the target.
The Dons were forced to make a change after 27 minutes when skipper Hartley limped off with an injury and was replaced by Derek Young.
Maguire was unfortunate not to double the home side's lead when he showed terrific skill to turn his marker before unleashing a powerful effort from the edge of the area that was clawed away by Paul Gallacher.
The visitors also made a change just before the break with Jure Travner, who had been booked, replaced by Kenny McLean.
Aberdeen got their second goal after 44 minutes when Vernon prodded the ball home after neat link-up play by Aluko and Steven Smith down the left.
St Mirren were forced to make a second change with less than five minutes of the second half played when Thomson had to be substituted because of a head knock and was replaced by Goodwin.
Aberdeen had the ball in the net for a third time after 54 minutes when Vernon outjumped Gallacher to head home but the goal was chalked off for a foul on the goalkeeper.
Vernon, the former Colchester striker, drew a smart stop from Gallacher before the visitors made their final change by bringing on Aaron Mooy for David van Zanten.
Ryan Jack, who had put in a tireless shift down the right flank, made way for Magennis with 13 minutes remaining.
Aberdeen introduced Vujadinovic for Aluko with less than five minutes remaining and the defender had the misfortune of heading the ball into his own net from a Darren McGregor cross with his first touch.
However the Dons held on to earn a return to the national stadium for a semi-final against the cup favourites.