Cooper brought up his century and remains unbeaten on 188 as the West End Redbacks piled on 180 in the middle session on day three at Junction Oval.
After digging in to reach 3-177 from 71 overs at lunch on Saturday, South Australia finished the day 5/527 off 136 overs in reply to Victoria's 6 (dec)-616.
Cooper brought up his ton with a straight six off spinner Jon Holland and celebrated the milestone with another six off the next ball.
He was 121 from 157 balls, with 15 fours and six sixes - one of which hit the window two floors up in the cricket centre at the city end.
Alex Carey had belted 91 from 98 balls, with 18 fours and a six, and the pair had raced to a fifth-wicket stand of 172 from 173 balls.
The Australian limited-overs vice-captain brought up his third first-class century with his 20th boundary of the innings.
The onslaught came from nowhere - when Redbacks captain Travis Head was dismissed for 51 after lunch, SA was teetering at 4-185 from 75.1 overs.
Already missing Aaron Finch for the day because of back spasms, Victoria suffered another injury after lunch when Nic Maddinson was forced from the field.
In the third over with the new ball, James Pattinson bowled a full toss and Cooper glanced a rocket to Maddinson at short leg.
As Maddinson turned to minimise the impact - he had no chance of taking the catch - it hit him on his right hand.
Maddinson, who top-scored with 224, did not return to the field after tea.
After SA resumed at 2-102, Henry Hunt reached 75 in what was an assured innings from the debutant, before Holland had him stumped.
Head played a gutsy innings for his 51 from 184 balls to see off a rested Victorian attack which found reverse swing in the morning, before Glenn Maxwell had him caught in slips.
Cooper will resume with allrounder Tom Andrews tomorrow (75*), who is currently on his highest first-class score.