Higdon struck after 41 and 65 minutes as Saints claimed their first points away from home this term to deny Dundee United a third straight success.
Prince Buaben powered in an 86th-minute free-kick to set up a tense finale, but United suffered a third home loss of the campaign.
United were seeking to build on victories over Hibernian and Hamilton, but in a limp display failed to test Saints goalkeeper Craig Samson until Buaben's late strike.
David Goodwillie came off the bench last Saturday to net the winner at Accies after spending time in police custody for an incident in Glasgow city centre last week.
But the striker, recalled to the starting line-up, was kept quiet by the visiting defence and United's poor quality in attack as his run of scoring in consecutive SPL matches was halted at six.
With Craig Levein naming his Scotland squad for next week's friendly with the Faroe Islands tomorrow, Goodwillie was among the players looking to impress.
But a poor first half was enlivened only when Higdon netted after 41 minutes.
The visitors had numerous half-chances before taking the lead.
Higdon shot tamely wide from 20 yards after being presented with the ball by United captain Garry Kenneth - capped by ex-United boss Levein in August's friendly with Sweden - midway inside the hosts' half.
The Buddies had another chance when Jure Travner whipped in a left-footed cross and Gareth Wardlaw at the far post headed into the side netting.
Scott Robertson fired narrowly over from 25 yards for United, before Higdon's backwards header looped high and off target.
Saints were forced into an early change after 30 minutes, with Sean Lynch replacing Hugh Murray, who appeared groggy after a clash of heads.
But the change in personnel did not impact on the visitors, as Higdon capitalised on a defensive error to put them in front.
Sean Dillon slipped and missed a long ball forward and Higdon took possession before tucking a clinical finish into the bottom right corner from 12 yards.
Kenneth was booked for a late lunge on Paul McGowan early in the second half before United manager Peter Houston sought fresh attacking impetus with the introductions of Ryan Dow and Jon Daly, who netted an 89th-minute leveller when the teams drew 1-1 in August.
Goodwillie then had a header held by Samson from Scott Robertson's right-wing cross after 63 minutes before Saints struck for a second time two minutes later as Kenneth's fraught evening continued.
McGowan kept the ball in on the right, hit an accurate, deep cross which Kenneth mis-judged and Higdon, with time and space, controlled the ball on his thigh before powering in beyond United goalkeeper Dusan Pernis from 16 yards.
United finally had an effort on target four minutes from time and Samson was beaten.
John Potter was booked for a cynical challenge as substitute Johnny Russell raced forward and Buaben powered the resulting 30-yard free-kick into the top corner.
But Saints held United at bay in three minutes of added time as the visitors claimed a deserved win.