South Australia need eight wickets and hold a lead of 101 runs after Sayers' maiden first-class 50 drove the Redbacks to 230 in their second innings.
James Pattinson (3-24) went through the Redbacks' top order on Monday's third day before a stunning late fightback from tailender Sayers.
Chasing a target of 124 to win, Victoria lost Marcus Harris (7) and first-innings century-maker Peter Handscomb (2) to speedster Joe Mennie, during a tricky 12-over period before stumps.
Travis Dean (10) and Cameron White (2) were able to guide their side to 2-22 at the close of play.
Melbourne's volatile spring weather might be a factor on Tuesday with rains and thunderstorms forecast.
Opener Conor McInerney batted superbly for his 63 off 146 balls and he combined with skipper Jake Lehmann for a 68-run partnership with SA in trouble at 2-43.
Pattinson then intervened to remove Lehmann who was caught by Travis Dean at gully on 22.
Fresh from back-to-back centuries, Tom Cooper strode to the crease but chopped a Pattinson delivery onto his stumps to depart for a duck.
Victoria were bowled out on Monday for 351 with a first-innings lead of 107 just 20 minutes after the resumption of play.
Handscomb (123 off 216 balls) turned the match in his side's favour with a gutsy century but he was dismissed with the first ball he faced on Monday morning.
SA won the toss but were all out for 244 on day one with Scott Boland (7-54 from 17 overs) doing the damage.