Cooper's superb ton came off 147 balls and included 18 fours and a six to help his side to 4-231 at tea, but they lost 6-13 after the resumption of play to be all out for 244.
The score was Cooper's second century in as many innings, after the right-hander made 178 against Queensland at Adelaide Oval last week.
But it was Victorian quick Boland who hurt SA when he took 5-8 in four overs at the start of the third session to finish with 7-54 off 17 overs.
Victoria are 0-72 at stumps, with Travis Dean on 56 and Marcus Harris on 16.
Boland removed danger man Cooper for 118, after dropping him at mid-on when he was on 80 and swiftly moved through the tail.
Having won the toss, the Redbacks were in early trouble at 3-45, but Cooper and skipper Jake Lehmann steadied the ship with a 98-run partnership.
Lehmann (56 off 101 balls) was in fine touch but dragged a wide delivery from Boland back onto his stumps 20 minutes after lunch.
Under overcast skies and with tinges of green grass across the pitch, the Victorian quicks made the most of the conditions in the morning session.
Returning Test quick Peter Siddle struck first, coaxing an edge from Jake Weatherald for five.
Callum Ferguson was adjudged LBW by Chris Tremain (1-63 from 17 overs) for three in the next over, despite the delivery appearing to have struck his inside edge.
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