Bancroft struck an unbeaten 105 off 255 balls as WA declared at 3-243 in their second innings, setting the Redbacks a victory target of 364 off 90 overs.
South Australia were precariously placed at 5-170 after 60.1 overs when a rain break wiped out 17 overs.
The loss of Harry Nielsen in the first over after the rain break meant WA needed just four more wickets with 12.2 overs remaining.
But Scott (33no off 106 balls) and Ben Manenti (21 off 34) guided the Redbacks to 6-208 before the game was deemed a draw with three balls remaining.
There was unexpected drama late in the match when Hilton Cartwright was forced off the field after being accidentally struck in the head by the ball.
Cartwright wasn't looking when Bancroft tossed the ball to him from five metres away, but luckily the impact was only minor.
Form is temporary, ����� �� ��������� 💫🙌 Bangers gets his 23rd — WACA (@WACA_Cricket) #SheffieldShield Century! � #WESTISBEST pic.twitter.com/MJ4GbVDcuvNovember 26, 2024
Bancroft started the season as a genuine chance to win the vacant opener's spot in the Test side following two mammoth years with the bat.
But his form turned to mush so quickly over the past two months that critics even started questioning whether he deserved to keep his spot in the WA side.
Bancroft opened the Shield campaign with scores of 0, 0, 8 and 2.
In his two matches for Australia A, which effectively doubled as a bat-off for the vacant top-order spot in the Test team, Bancroft scored 0, 16, 3 and 0.
Nathan McSweeney ended up winning the Test call-up, and Bancroft went on to make 12 and 11 in his next Shield match against Victoria, before opening the current Shield clash with a first-ball duck, despite not appearing to have edged the ball.
It continued a rotten run of luck for Bancroft, with a number of his dismissals this season appearing to be umpiring errors.
But his luck finally changed.
Bancroft made it to stumps on Monday unbeaten on 71, and he had one edge fall short and another edge fly too high for the fielder on Tuesday on the way to reaching his 30th first-class century.
Cameron Bancroft's reaction says it all as he brings up his first ton of the summer! — cricket.com.au (@cricketcomau) #SheffieldShield pic.twitter.com/xasKYfjNY0November 26, 2024
The 32-year-old raised his bat and helmet to the sky upon reaching triple figures, with the knock an important step in his bid to get back in the conversation for a Test call-up.
WA young gun Jayden Goodwin was named man of the match for his scores of 139 and 69.
