South Australia 159 and 8 for 218 (Head 72*, Kelly 4-55) lead Western Australia 157 (Winter 4-23) by 220 runs
A fighting unbeaten 72 from South Australia captain Travis Head helped the Redbacks propel their lead beyond 200 against Western Australia at the WACA.
Head became the first player in the match to pass 50 and remained unbeaten at stumps alongside Daniel Worrall after Warriors paceman Matt Kelly had taken four wickets.
The Redbacks started their second innings with a lead of two runs after left-arm seamer Nick Winter claimed 4 for 23 to wrap up WA's first innings. five Redbacks opener Jake Weatherald fell early, caught behind off Kelly for 5, before Conor McInerney and Jake Lehmann prospered with a 67-run stand.
Much like the first innings, Hilton Cartwright was called into the attack to make the breakthrough, and it worked as McInerney fell caught behind within sight of 50 for the second time in the match.
Lehmann was Kelly's second scalp for 30 before Cartwright picked up another, rattling Callum Ferguson's stumps.
But Head stood firm as wickets tumbled at the other end. Kelly was on a hat-trick at one stage but the Redbacks skipper kept the scoreboard moving, reaching a fluent half-century that featured 11 boundaries.
He found an ally in Worrall as the pair put on 39 in the last 12.3 overs of the day to reach stumps unscathed with a lead of 220.
Earlier, Winter and Worrall took the last six wickets between them to leave the Warriors all out for 157 with a two-run first-innings deficit.
Winter bowled nightwatchman Kelly early in the day before Cartwright and D'Arcy Short both fell caught in the slips driving at Worrall. Josh Philippe rode his luck for an enterprising 47. He hooked a six but was fortunate that three outside edges found the third-man boundary as South Australia opted for only two slips instead of three.
Philippe and Joel Paris put on 51 for the eighth wicket and looked set to give WA a lead but Winter picked up Paris and Liam Guthrie in three balls before Philippe holed out to mid-off an over later off Worrall.