Left-armed paceman Johnson (4-63) narrowly missed a hat trick earlier when he had Prasanna Jayawardene caught by Hughes at third slip for 24 while fending off a short ball, then had Prasad caught behind the next ball.
The dismissal of Prasanna Jayawardene broke up a promising 35-run partnership with Sangakkara and exposed the Sri Lankan tailenders to an increasingly confident Australian pace attack.
"It was a disappointing day unfortunately, perhaps a few poor decisions made by some of our batters," said Sri Lanka coach Graham Ford, whose squad won the toss and elected to bat.
"Unfortunately we find ourselves behind the game by quite a way and we're going to have to fight back hard."
Seam bowler Jackson Bird secured his first wicket in his maiden test in the fourth over of the match to spark a top-order collapse when Dimuth Karunaratne lunged forward and was caught behind for 5.
Peter Siddle returned figures of 2-30, while spin bowler Nathan Lyon mopped up the Sri Lankan tail to finish with 2-23.
"I think Sri Lanka out within 44 overs was an unbelievable effort," Johnson said. "Obviously Jackson Bird on debut performed very well ... and started us off in the morning."
Sangakkara reached the 10,000-run mark in 195 innings, equaling the record previously shared by Brian Lara and Sachin Tendulkar. Tendulkar tops the test run scorers list with 15,645.
Sangakkara averages more than 55 runs in a career spanning 115 tests. The only other Sri Lankan to have made more than 10,000 test runs is Mahela Jayawardene.
After a race to prove his fitness, Australia named Clarke to play despite the hamstring injury he suffered in last week's first test in Hobart.
"I'd call myself 100 percent (fit)," Clarke said during the coin toss. "If I couldn't have turned up today and performed at my best, I wouldn't have been playing."
