Sri Lanka's injury woes worsened on the second morning when paceman Chanaka Welegedara pulled up while running in to bowl to Clarke and limped from the field. He left the grounds for scans on his hamstring.
The visitors lost regular wicketkeeper Prasanna Jayawardene to a fractured right thumb on Wednesday, his place behind the stumps being filled by Sangakkara.
Johnson claimed four wickets Wednesday to help dismiss Sri Lanka in under two sessions.
The only highlight of the Sri Lankan innings was a defiant 58 from Sangakkara that included his 10,000th test run.