Dargo marked his return to the starting line-up by making two and scoring one as Higdon, who struck a hat-trick in last Saturday's 3-1 win over bottom club Hamilton, set the ball rolling with a half-volley after six minutes following his strike partner's flick-on.
Aberdeen netted a 46th-minute equaliser when Chris Maguire's effort deflected in off Hugh Murray, but Dargo tucked in a 57th-minute second before setting up Thomson in the 68th minute.
Rob Milsom netted a fierce low drive from 25 yards after 90 minutes but Saints held on to claim back-to-back victories for the first time this season.
With seven matches of the season remaining, including at Celtic and Rangers in the next two games before the SPL split, Saints hold a 12-point lead over Accies, who now appear all but doomed to relegation.
Ninth-placed Aberdeen are now three points clear of Saints, who overcame the loss of Lee Mair following the warm-up to make a strong start in the contest, which was their game in hand over Accies.
The Dons progressed to the Scottish Cup semi-final at the expense of St Mirren last month and the hosts were out for revenge.
After six minutes the Buddies went in front when a long ball forward was headed on by Dargo.
Higdon was in space just inside the visitors' penalty area and struck a sweet half-volley for his 15th of the season.
Maguire, who was lively throughout, tried an audacious chip which never troubled Paul Gallacher in the hosts' goal before firing narrowly wide from 30 yards.
Andrew Considine headed onto the roof of Gallacher's net from 18 yards before Michael Paton hit a shot into the ground which the Buddies goalkeeper held.
Aberdeen applied pressure but Saints were untroubled until the interval. However, within 60 seconds of the restart the visitors were level.
After Peter Pawlett had forced Gallacher into a smart save, the winger took the resulting corner short. Maguire collected the ball on the left of the Saints area and hit a shot from an acute angle which deflected inside the far post off Murray.
McArdle was replaced by Ryan Jack with an apparent arm injury before the visitors suffered another blow when Saints went in front for a second time.
Aaron Mooy found Higdon, who laid the ball off for David van Zanten to cross and Dargo was unmarked at the far post to tuck in from close range.
Jamie Langfield held a Thomson shot from 18 yards soon after and then Considine was booked for bringing down Paul McGowan as he surged through the middle.
Saints were looking confident and Dargo was once again the provider for their third after racing inside the left of the area.
The striker pulled the ball back and Thomson calmly slotted into the bottom corner for Saints' third.
Aberdeen continued to press forward and Scott Vernon replaced Josh Magennis up front but Saints stood firm with men behind the ball.
Milsom finally breached their defence with a fierce left-foot shot from 25 yards into the bottom corner but Saints survived a nervy stoppage time.