Davis dug in for the West End Redbacks on the third day of play at Karen Rolton Oval to put on 63 runs for the fifth wicket with SA skipper Travis Head (37).
He then joined with wicketkeeper Harry Nielsen (40) for a 64-run partnership to rescue the Redbacks from 4/39 in the first session.
The 29-year-old compiled 52 runs from 137 deliveries and stroked six boundaries in a glimpse of his talent.
Victoria resumed with the bat in the morning on Day Three at 8/240 but added just six more runs before the ninth wicket fell, spelling the end of their innings with injured batsman Nic Maddinson already ruled out of the remainder of the match.
South Australia reached 192 in reply, setting the visitors 167 to win.
Chris Tremain was Victoria’s most damaging bowler with figures of 4/34 from his 12 overs.
The Vics then raced to 0/69 at stumps to put themselves in the box seat courtesy of openers Travis Dean (33*) and leading Shield runscorer Marcus Harris (36*).
Victoria require 98 runs on the final day to notch a sixth victory ahead of next week’s Shield final while the Redbacks need nine wickets to record a last-gasp win.
STUMPS ⏰— West End Redbacks (@WestEndRedbacks) March 22, 2019
We'll be back for the final day of our 2018-19 #SheffieldShield campaign tomorrow
VIC 0/69 require 98 to win, we need 9 wickets - scorecard 📊: https://t.co/vCy5VzqMbp #SAvVIC pic.twitter.com/qaG7F6cYyf