Tillakaratne's form slumped after taking over the captaincy last year. His average in the last 12 innings before Friday was 16 with a highest score of only 45.
The 36-year-old has been widely tipped to be replaced as captain following the Australia series after winning just one Test in a nine-match tenure.
But Tillakaratne produced a fighting riposte to his critics, batting for 271 minutes and 201 balls as he steered Sri Lanka to a slim six-run first innings lead on the third day.
"It was very important and I rate this innings as good as my 136 I scored against India [in 2001] when I came back after two-and-a-half years," Tillakaratne told reporters.
"I thought that was my last innings but I managed to get a hundred there."
He added: "When I read the newspapers, there were so many things said and done and I went in there thinking it was my last innings.
"I just played my normal game and wanted to be there as long as possible and make a big score. Until I got about 30-odd I was struggling a bit but after that I was okay.
"We all know that I had a lean period but after this knock I should be able to get more runs. If I am not scoring I don't want to be a liability to the team."
Tillakaratne believes Sri Lanka, who grabbed three Australia wickets in the final session, can chase a target of 250 in the last innings to win the match and prevent an Australian whitewash.
He said: "There are two more days to go and we have to pick up early wickets tomorrow. The wicket is starting to take turn and it will definitely help our spinners."
