Set 233 to win at Bankstown Oval on Friday, the Bushrangers always had the target covered and got home with 13 balls to spare.
White (86 off 89 balls) was selective in his hitting, smashing six fours and four sixes.
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It was almost a year to the day since his last appearance for Australia in the World Twenty20 semi-finals.
"I definitely want to play for Australia in all formats again," White told AAP.
"It's been a focus of just making sure I get back into a bit of form.
"I feel as though I've done that last summer and then through the winter and hopefully I can carry that onto the rest of the season."
White had only been back in Australia for two days after a stint in English county cricket.
The Bushrangers have emerged as the early pacesetter in the one-day competition, winning each of their first two games.
"There's only six games (for each team), so we spoke about wanting to really hit the ground running, and we've done that," White said.
The Redbacks also had two half century stands, but no batsmen reached 50.
"Partnerships is always the key they showed that," Redbacks captain Johan Botha told AAP.
"Rob Quiney and Cameron White were probably the difference on the day.
"We got 30s and 40s, they got 60s and 80s," he said.
Hughes and Michael Klinger (33 off 52) got the Redbacks off to a flyer with an opening stand of 69 off 15.3 overs.
A late innings sixth wicket stand of 64 between topscorer Sam Miller (47 not out off 67 balls), who was making his one-day debut for the Redbacks, and wicketkeeper Tim Ludeman (38 off 42) ensured SA made the first score of over 200 in three matches at the venue this season.
The next competition game on Monday at Bankstown will pit Victoria against NSW, who have won their only match to date against Tasmania.