Needing 351 to win, South Australia were bowled out for 244 in their second innings an hour into day three's final session on Tuesday.
It was Western Australia's third outright win in five games but it was not enough to lift them out of third position on the table. They are, however, within striking distance of top sides Queensland and New South Wales.
Former Test batsman Greg Blewett gave the home side hope with a patient 80 along with 48 from youngster Callum Ferguson, but for the third time in as many days, Hogg swung the match.
He took a brilliant low catch off his own bowling from a full-blooded drive to remove Ferguson and then followed that with the prized wicket of Blewett, bowled attempting a sweep shot, to finish with figures of 3-46 to go with his first innings century and 61 in the second dig.
Victorian skipper Cameron White hit a maiden first-class century to put the champions in the driver's seat against Queensland at the Gabba.
White belted fellow Indian Test series tourist Nathan Hauritz for a boundary and then a six over long-on off successive balls to notch his ton just before stumps on the third day.
Victoria dominated the day to take their second innings score to 472 for six and hold a 289-run lead with four wickets in hand.
Opener Jason Arnberger led the turnaround after the Victorians were forced to follow-on, by scoring 152 in six hours.
White (105 not out) and Ian Harvey (71 not out) combined in an unbeaten 179-run seventh-wicket stand. Andy Bichel took 4-90 off 27 overs.