Faced with a daunting target just to make Australia bat again, Dimuth Karunaratne was run out for 1 by Johnson off a David Warner relay with the third ball of the second innings.
Tillakaratne Dilshan fell for a duck off Johnson's next ball when he was caught by Ed Cowan at short leg.
Debutant paceman Jackson Bird claimed a wicket in the very next over when Mahela Jayawardene (0) looked to leave the ball, only to watch it deflect onto his stumps and leave Sri Lanka at 3-3.
Thilan Samaraweera added just 1 run before being trapped lbw by Bird (2-10).
Sangakkara (27) looked to be settling in before retiring shortly after lunch after taking a Johnson delivery on his left index finger.
He left the field for scans and did not retake the field.
Angelo Mathews then played a rash shot at a seaming Johnson delivery and dragged the ball onto his stumps for 35, exposing the Sri Lanka tail.
