Renshaw finished 156 not out as Queensland reached 4-275 from 42.1 overs, after Sandhu's hat-trick, his second in his one-day career, inspired a SA collapse after they had seemed set to post a big total.
Redbacks wicket-keeper Alex Carey had a century in the bank and the home side looked capable of a sizeable score before Sandhu became just the second Queensland bowler to take a hat-trick in List A cricket.
It saw South Australia lose 6-9 to be dismissed for 274 in the 48th over.
Sandhu, who has forced his way into the Bulls line this season after relocating to Brisbane last year, joins Nathan Rimmington who claimed his hat-trick against WA at the Gabba in 2009-10.
It was Renshaw's highest one-day score and his first List A century for Queensland.
He and Max Bryant (68) put on 177 for the fourth wicket.
The Bulls six-wicket win lifts them into second spot on the Marsh One Day Cup ladder as the one-day and Sheffield Shield competitions go into hiatus ahead of the start of the KFC Big Bash League next week.