After the opening day of the pink-ball fixture was washed out, SA's Thornton and Manenti both claimed three wickets as WA struggled to 188 all out on Sunday.
The South Australians reached 1-100 at stumps at Adelaide Oval, with Henry Hunt not out 42 and captain Nathan McSweeney on 33.
In WA's innings, Jayden Goodwin top-scored with a fighting 53 from 106 balls and Cooper Connolly (33) and Aaron Hardie (31) chipped in.
But the trio were the only three batsmen to pass 17 amid a miserly display from SA paceman Thornton, who returned superb figures of 3-25 from 14 overs.
Thornton took the initial two wickets, removing Sam Whiteman (14) and Cameron Bancroft (nine).
And when Jordan Buckingham (2-33) dismissed Hilton Cartwright  for five, the visitors were wobbling at 3-51 in the 25th over.
Spinner Manenti captured three of the next four wickets, including ending an innings-high 68-run partnership between Goodwin and Connolly.
The WA duo fell within a three-over span and the visitors lost their last seven wickets for 69 runs.
SA openers Hunt and Connor McInerney (18) navigated a dozen overs before WA quick Liam Haskett (1-27) broke their stand.
Skipper McSweeney immediately showed intent by hitting a four from his first ball and was in fine touch, striking three more boundaries in his 56-ball knock and combining with Hunt for an unbroken 67-run partnership.
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