Maguire's magnificent volley from 25 yards in the 28th minute was one of the few highlights in a scrappy game at Pittodrie.
The young Aberdeen striker spurned a number of opportunities in the second half to get a second but the Dons held on for a deserved win on a very blustery day at Pittodrie.
The Dons made two changes to the side that drew 1-1 with Dunfermline in last weekend's Homecoming Scottish Cup quarter-final.
Javan Vidal returned to the Aberdeen defence in place of Stuart Duff, while the more attack-minded Maguire was preferred to Derek Young.
Injury and suspension problems meant Billy Reid was forced to make five changes to the Hamilton starting 11.
James McArthur returned from a knee injury to replace the suspended Simon Mensing in midfield.
Jordan McMillan, Joel Thomas, Derek Lyle and Martin Canning also started in a makeshift Academical side with top scorer Richard Offiong only fit enough to start from the bench.
Despite their impressive home record, the Dons had not won in the league since their 4-2 win over champions Celtic in January but created the first real opening of the match.
Tommy Wright, who had already picked up an early booking, was picked out with an intelligent pass from Jamie Smith but Martin Canning made a crucial block. Charlie Mulgrew almost opened the scoring direct from the resulting corner kick but Tomas Cerny managed to scramble the ball clear.
Zander Diamond was then inches away from connecting with a Smith corner in the 17th minute with the blustery conditions and poor pitch doing little to aid the game as a spectacle.
However the Dons did take the lead in the 28th minute thanks to a wonderful strike from Maguire. The young striker volleyed the ball home from 25 yards to give Cerny in the Hamilton goal no chance.
Aberdeen were noticeably lifted from the goal and Scott Severin found Sone Aluko who should have doubled the lead but his initial effort was blocked by Canning and his second attempt was thwarted by Mark McLaughlin.
Paul McGowan almost capitalised on some hesitant defending in the Aberdeen box after 36 minutes but dragged his shot harmlessly wide of the target.
Aberdeen made a change at the interval with Richard Foster replacing Vidal at right-back.
Jordan McMillan picked up a harsh booking in the 52nd minute for upending Aluko in a scrappy start to the second period.
The Dons almost grabbed a comical second when Smith sportingly played the ball back to Cerny after a Hamilton player had been injured but the goalkeeper was not paying attention and had to make a frantic dash to prevent the loose ball crossing the goalline.
The home support were screaming for a penalty after 57 minutes when Wright fell in the box under pressure from McLaughlin but referee Euan Norris waved play on.
Maguire should have got his second when Smith found him with an accurate cross from the right but Cerny tipped the young striker's header over the bar.
With Canning off the park receiving treatment, Maguire had another opportunity when he muscled his way past stand-in centre-half Kenny Deuchar, who had earlier replaced McGowan, but the Dons forward blasted the ball into the side-netting.
The omnipresent Maguire then drove at the Hamilton defence before unleashing a powerful left-footed drive from distance but Cerny made a comfortable save.
Richard Offiong came on for McArthur with only four minutes remaining as the away side went for broke.
But the Aberdeen rearguard held firm to ensure they picked up three vital points in their quest to qualify for next season's Europa League.