South Australia 116 for 3 (Lehmann 37*, Fraser-McGurk 26*) trail Tasmania 195 (Kellepotha 50, Buckingham 4-49) by 79 runs
Batting at No.8, Kellepotha top-scored with 50 as Tasmania could only manage 195 after winning the toss on Friday.
They slumped to 86 for 6 before Jake Doran made 44 at No.6 and tailender Gabe Bell posted his highest first-class score of 27.
Buckingham led the attack with 4 for 49, and South Australia at stumps were well-placed at 116 for 3.
Jake Lehmann had made 37 and Jake Fraser-McGuirk was also looking well-set on 26.
Kellepotha moved from Sri Lanka, where the legspinner played first-class cricket, in 2013.
The 34-year-old played one Shield game for Victoria, and also had three games with the Melbourne Renegades in the BBL, but moved south ahead of this season and broke into the Tasmanian team.
He hit two fours and three sixes in his 104-ball innings. Lehmann gave him a life on 31 when he dropped a chance in the deep off legspinner Lloyd Pope.
SA player Hanno Jacobs had to leave the field after he was hit on the head while trying to take a catch. He was later cleared of injury.
Billy Stanlake snared the wicket of Jason Sangha to leave the home side in early strife at 63 for 3.
But Lehmann, who scored at faster than a run a ball, and Fraser-McGurk batted through to stumps. Tasmania must break up their partnership early on Saturday to have any hope of a first-innings lead.
SA fielded a recast batting line-up, with captain Nathan McSweeney away on Australia A duties. Tasmania similarly made several changes because of injury and national commitments.
After five games, SA are fourth on the Shield ladder in their title defence with only one win, and Tasmania are third.