Aberdeen took full advantage of Celtic's surprise defeat at the hands of Kilmarnock to cut the gap at the top of the Ladbrokes Scottish Premiership to eight poi
In a match that could hardly be described as a classic, the Dons did enough to take the points, despite a spirited rearguard action from Martin Canning's Hamilton side.
Andrew Considine led the charge for the Dons, netting a double, with Niall McGinn also on the scoresheet.
Indeed, when the defender turned in the area to hook home a right-footed effort after the Hamilton defence had failed to deal with McGinn's free kick, it was the first real chance either side had created.
McGinn himself had an effort five minutes later, flicking a half-volley towards goal from 18-yards, but Woods was able to gather and hold at the second attempt.
That sparked a period of dominance for the Dons, with Considine heading wide and Adam Rooney sending a close range header over the bar from a Ryan Christie corner. But despite looking comfortable, the home side never seriously looked like adding to their tally before the interval.
After scoring a goal of the season contender last week, central defender Scott McKenna has previous for shooting from distance, and he tried his luck from 25-yards five minutes after the break. His effort was deflected and an awkward bounce forced Woods to push over the crossbar.
The Hamilton captain was certainly the busier of the two goalkeepers, with Aberdeen's loan signing Freddie Woodman having little to do on his debut.
Indeed, Woods would not have thanked central defender Xavier Tomas for his wayward header on the hour mark, the looping ball forcing the keeper into another awkward save.
Midway through he second period, McGinn cut in from the left flank and snatch a shot at goal, with Woods getting down low to his left to turn round the post.
But the goalkeeper was finally beaten 10 minutes from time as McGinn rifled in the second goal of his second spell at Pittodrie after Kenny McLean's right wing cross was only half-cleared by the Hamilton defence.
And the Dons added a third with three minutes remaining as Considine rose at the back post to head home his second of the afternoon, meeting a right wing cross from Ryan Christie, after the on-loan Celtic man had combined neatly with McGinn.
They could have added a fourth, but substitute Nicky Maynard was denied by Woods, who raced off his line to prevent the former Bristol City man netting his first Dons goal.