He connected sweetly with a cross from opening scorer Charlie Mulgrew to secure the three points with half an hour of the game remaining.
Mulgrew had put the Pittodrie side in front with a first-half free-kick, and then fired in another set-piece five minutes later from which Andrew Considine doubled the lead at the interval.
Accies hit the post just before half-time and rallied briefly at the start of the second half, but otherwise never troubled their opponents.
Hamilton manager Billy Reid handed debuts to two more players as he made three changes to his side.
Marco Paixao took his place in the team alongside twin brother Flavio, who made his bow at Kilmarnock a week earlier, to be joined up front by teenage debutant Kyle Wilkie.
Martin Canning returned from suspension while Marvin Andrews and Derek Lyle dropped to the bench, where they were joined by new arrival Leon Knight.
Visiting manager Mark McGhee made four changes to his team as they, like the hosts, sought to register their first points after opening-day defeats.
Youngsters Jonathan Crawford and Fraser Fyvie were handed starts while Considine and Darren Mackie were promoted from the bench; Zander Diamond and Gary McDonald both failed to recover in time from knocks and Stuart Duff and Maguire were both among the substitutes.
Lee Miller tested home goalkeeper Tomas Cerny in the first minute with a turn and shot from Sone Aluko's pass, but Cerny stooped to claim it without fuss, while Mackie then sent a shot wide of the left-hand post.
Mulgrew then drilled a shot which was smothered at the left-hand post, and Aluko's acute-angled shot from the left was touched onto the roof of the net.
Wilkie had Hamilton's first effort with a free-kick from the left touchline which curled straight into Jamie Langfield's arms.
Flavio Paixao was booked and conceded a free-kick just outside the box when he tracked back to tackle Richard Foster, but Miller's effort was blocked by the five-man wall.
Mulgrew was more successful on 23 minutes, however, curling a 25-yard free-kick from just outside the right-hand side of the box in at the near post.
Aberdeen doubled their lead five minutes later with a goal stemming from another set-piece.
The visitors were awarded a free-kick wide on the left after a challenge for which Wilkie was booked. Mulgrew floated it across goal and Andrew Considine was on hand at the far post to beat Izzy Irekepn and decisively slot the ball home from close range.
Mackie could even have added a third goal before half-time when the ball was whipped across the face of goal, but Cerny managed to gather it off his toes.
However, Hamilton were unfortunate not to score from their first serious effort on goal two minutes before the break.
Wilkie fired in a free-kick from the left wing which hit the opposite post - Marco Paixao responded instantly to the rebound but his effort was cleared off the line by Considine.
Hamilton made two half-time changes, replacing Wilkie and Kissock with David Louhoungou and Knight respectively.
Straight from kick-off, Flavio Paixao bore down on goal and, although he was forced out wide, passed to James Wesolowski who set up Simon Mensing for a shot which Aberdeen scrambled to block. Knight's first touch was a diving diagonal header which went wide of the left-hand post.
However, Aberdeen made it 3-0 in real style just after the hour. The visitors retained possession after good work and a weaving run into the box by Aluko and, from Mulgrew's cross, substitute Maguire unleashed a sweet volley from the right corner of the six-yard box which flew into the net.
Aluko came agonisingly close to making it four for the visitors with a drilled diagonal effort which whistled narrowly wide of the right-hand post, and a Mulgrew drive from Aluko's pass met the same fate.
Langfield had to bat a free-kick from Derek Lyle over the top of his goal with little over 10 minutes to go, but Accies were unable to cash in on the free header from Luis Rubiales' corner.
Untroubled Aberdeen saw out the closing stages with ease to claim the victory and leave the hosts still searching for their first goal and points of the new campaign.