Sangakkara - sixth ton in his last 12 Test innings.
Sri Lanka will chase a victory target 260 runs on the final day of the second Test against Australia with seven wickets remaining.
Looking to the level the series in Hobart, the team from the sub-continent has a fighting chance with Kumar Sangakkara still at the crease on 109 - his 15th Test century.
Australia declared three hours before lunch on Monday after adding 99 runs to their overnight score for a lead of 506.
Mitchell Johnson then stung Sri Lanka early when he dismissed Michael Vandort for just four right before the break.
The visitors frustrated the hosts, however, as Marvan Atapattu and Sangakkara guided Sri Lanka to 139 for one at tea.
Atapattu, playing in his first Test for nearly two years, produced a half-century off 94 balls and was 74 not out while Sangakkara was unbeaten on 51.
Atpattu only added six more runs to his score and headed back to the pavilion after hitting a Brett Lee delivery that was caught at deep midwicket by Phil Jaques with Sri Lanka 158 for two.
Lee struck with the very next ball, a yorker beating Mahela Jayawardene for a duck.
Sanath Jayasuriya helped steady the nerves by rattling off 33 with Sangakkara reaching his ton to take their partnership to 89 and leave the Test delicately poised heading into the final day.