Wildcats imports Casey Prather and Jaron Johnson led them back to within four, the Sixers clinching it from the free throw line.
"Our last quarter, we played really good defence," 36ers coach Joey Wright said.
"We need to tidy up the last couple of minutes.
"Sobey was big for us tonight.
"He's done a great job and is always aware of the defence out there.
"His intensity and his deflections were important."
The game was physical and nasty, with the referees dishing out technical fouls and Anthony Drmic suffering an eye scratch from an errant Jesse Wagstaff hand.
First half momentum shifted to the Wildcats when Randle, rightly riled after heavily being fouled by Wagstaff and again manhandled on the 36ers' next attack, collected a foul in Adelaide's next defence.
When referee Vaughan Mayberry hit him with a technical foul for dissent, Perth used the distraction to push further ahead, Prather with its next six points.
That was despite emphatically having shots blocked by Matt Hodgson and Terrance Ferguson during his sequence.
Johnson and Sobey held the fort in Randle's absence but Jaron Johnson and Prather had pushed Perth ahead 44-41 by halftime.
ADELAIDE 36ERS 78 (Sobey 24, Randle 22, Johnson 11) PERTH WILDCATS 74 (Johnson 21, Prather 18)