Wade began the day on 47 with Australia 6-342 in reply to Sri Lanka's competitive opening innings total of 294.
The dynamic wicket-keeper batsman batted well late on the second day, but was beginning to run out of partners with Peter Siddle joining him overnight not out on 16.
Siddle offered tremendous support on Saturday morning, though, hanging in there with Wade as he neared his second Test century.
When Siddle fell caught behind off Nuwan Pradeep for 38 it appeared Wade's chance might have gone with it, especially when left-arm spinner Rangana Herath quickly got rid of Mitchell Starc (2) and Nathan Lyon (4).
That left Jackson Bird at the crease with Wade nearing the ton and the Tasmanian quick showed some good temperament to remain six not out as Wade brought up the century in stunning fashion with a hook shot for four.
He remained 102 not out from 158 balls with his innings including nine fours as he recorded his first century on Australian soil after his maiden Test ton came last year in the West Indies.
That saw Wade achieve what Sri Lanka's Mahela Jayawardene (72) and Lahiru Thirimanne (91), and Australia's David Warner (85) and Phil Hughes (87) weren’t able to do in reaching triple-figures despite solid knocks at the crease.
After Wade reached the milestone, skipper Michael Clarke declared Australia's innings closed at 9-432 with a lead over Sri Lanka of 138 runs.
Herath, as expected on the SCG wicket, was the pick of Sri Lanka's bowlers finishing with 4-95 from 31 overs. Pradeep was also a solid contributor with 2-114 and Tillakaratne Dilshan was the only other wicket-taker with 1-58.
Clarke's declaration also gave Sri Lanka's openers an awkward 20-minute period to bat before lunch, but Dimuth Karunaratne (17) and Dilshan (0) did well to survive two overs each from Starc and Bird to be 0-18 at lunch with a 120-run deficit still.