The tourists weathered seven overs to reach the break at 21 without loss with Tillakaratne Dilshan, who had made eight not out, and Dimuth Karunaratne, who was unbeaten on 13, set to resume for the final session.
Early morning showers delayed the start of play at the Bellerive Oval by 50 minutes and there was a further 80-minute disruption after lunch but Hussey and Matthew Wade (68 not out) did their best to make up for lost time.
Sri Lanka's Shaminda Eranga had struck early to take the key wicket of skipper Michael Clarke for 74 on the 13th ball of the day but their much pilloried pace attack struggled to make further inroads into the Australian order.
Hussey reached his 19th test century in fortuitous circumstances when he was dropped at deep midwicket by Angelo Matthews and the ball bounced across the boundary rope for four.
It was not the 37-year-old's most fluent innings – coming off 171 balls with most of his eight fours struck after he reached the half century – but it could turn out to have a significant bearing on whether a result is achieved in the test.
In the previous over, wicketkeeper Wade had reached his own half century with a rushed single as he further cemented his place in the Australia team after his 68 in the last test against South Africa.
Clarke had managed to add just four runs to his overnight tally of 70 before a delivery from Eranga induced him into an edge which Kumar Sangakkara collected with ease at second slip.
It was an key wicket as he and Hussey have now put on 736 runs in partnerships over the last four tests but it was to be a sole success for a pace attack dubbed the worst to tour Australia by former test player Rodney Hogg this week.
Wade looked less assured early on, especially with some of his run calling, and he survived an optimistic lbw appeal from Chanaka Welegedara when the TV umpire confirmed the ball had pitched outside the line of the stumps.
There was another scare two overs later when Wade pulled a short delivery from Welegedara and replacement fielder Suraj Randiv just failed to hold a catch at midwicket.
The tourists have never won a test in Australia and will have two more attempts at breaking that duck in Melbourne and Sydney should they fail to win in Hobart. – Reuters