Queensland scored 8-273 before a confident all-round bowling effort saw South Australia routed for just 183, with the Bulls also picking up a bonus point.
The Queenslanders shared the spoils among five wicket-takers with off-spinner Nathan Hauritz claiming the best figures (3-31).
However, it was Harris, featuring in just his second match since a two-month break, whose performance was under the most scrutiny ahead of next month's first Ashes Test against England in Brisbane.
Despite a modest return of 1-36 off eight overs, Harris bowled with good speed and bounce under the watchful eye of Australia coach Darren Lehmann.
Harris, who starred in Australia's 3-0 Ashes series loss in the UK prior to injuring a hamstring, said his bowling and fitness were still a work in progress.
"It felt better today than the other day," he said.
"I still have a bit of work to do and a lot more bowling to do yet and the more I do the better I should get."
Harris picked up the early wicket of Michael Klinger, the competition's highest run-scorer helping to kick-start a steady flow of wickets.
Cutting, having played a stunning knock of 98 not out off 48 balls at the same venue last weekend, seemed set to repeat the dose before skying into the deep after striking four sixes and facing just 30 balls.
Hopes also batted intelligently, scoring at nearly a run-a-ball while opener James Peirson top-scored with 85 off 102 deliveries.
Despite the small ground it was spin that made the difference for South Australia in the middle part of the Queensland innings.
Redbacks skipper Johan Botha claimed three quick top-order wickets with his off-spin before finishing with 3-42 off ten overs.
The immediate playing future of the South African all-rounder is set to be determined this week after he was recently reported for a suspect bowling action.
Former NSW leg-spinner Zampa took 2 for 28 off eight overs.
"I thought we did well to restrict them to 270, so a positive bowling and fielding effort but we let ourselves down with the bat," said Zampa.