The goal came after 30 minutes at Pittodrie after Sone Aluko had been fouled in the box by Jim McAlister and Maguire stepped up to score his ninth goal of the season.
Hamilton enjoyed plenty of possession in the second period but were unable to find a way past a resolute home defence.
The result heaps further pressure on the Accies, who have not won in the league since October and remain five points adrift of St Mirren at the foot of the table.
Aberdeen skipper Paul Hartley and defender Andrew Considine returned from suspension but both had to be content with a place on the bench as Craig Brown stuck with the same side that defeated Kilmarnock 5-0 on Saturday.
Accies welcomed back Dougie Imrie from injury and former Don Gary McDonald was also given a start against his former club, with Mark Carrington dropping to the bench and James Chambers missing out.
The visitors had an early chance to test Jamie Langfield in the Aberdeen goal when Gavin Skelton found Flavio Paixao, who evaded the challenge of Zander Diamond with a neat touch before curling the ball harmlessly over the crossbar.
The Accies would have been encouraged by their lively start but should have fallen behind after 13 minutes when David McNamee crossed for the unmarked Aluko at the back post, only for the Nigerian international to volley wide.
The Dons survived a scare of their own after 21 minutes when Imrie’s inviting free-kick into the area was headed over by Mickael Antoine-Curier.
A slack pass by Rory McArdle gifted the visitors another chance but Imrie fired wide of the target after being released by Antoine-Curier.
And with 30 minutes gone Aberdeen had the chance to make the breakthrough when Aluko was fouled in the box by McAlister.
With Hartley on the bench, Maguire assumed the spot-kick duties and smashed the ball into the bottom corner past Cerny.
The Dons almost doubled their lead two minutes before the break when a fizzing corner from Aluko was headed wide by the unmarked Diamond, who should have at least tested the goalkeeper.
Aberdeen almost made the perfect start to the second period when Maguire dispossessed Martin Canning before laying the ball into the path of Robert Milsom, whose shot curled just past the post.
Hamilton had an excellent chance to equalise after 50 minutes, but Imrie shot straight at Langfield instead of squaring the ball to Antoine-Curier who would have had the easiest of finishes.
Hamilton were enjoying an increasing amount of pressure as the half wore on with the home side introducing Hartley for Derek Young to stem the tide after 63 minutes.
The Accies made an attacking change by bringing on striker Nigel Hasselbaink for defender Mark McLaughlin, but the match should have been put beyond doubt when Maguire pounced on a mistake by David Elebert only to fire wide.
Maguire spurned another opening with 12 minutes to go when he latched onto Milsom’s pass, but his effort squirmed past the post.
Vernon drew a smart stop from Cerny before Langfield did well to hold onto Imrie’s rasping free-kick at the other end as a frantic and entertaining match came to a close.