A late arrival on United's pre-season tour, Van Persie was only introduced for the final half hour after a heavy week's training.
But it was long enough to claim the assist for Danny Welbeck's second before atoning for an uncharacteristic miss by driving home from close range almost immediately afterwards.
After the false start in Bangkok last weekend, it completed a satisfactory evening for the Red Devils, who fly to Japan on the next leg of their tour on Sunday for matches in Yokohama and Osaka.
And for Moyes it was a welcome first win, with Warrington-born youngster Jesse Lingard having the honour of scoring United's first goal for their new manager in front of 83,127 at ANZ Stadium.
That an Australia national side missing its European contingent was facing South Korea in an East Asian Cup encounter at virtually exactly the same time as the remainder of the A League was in action underlined the scratch nature of Ange Postecoglou's team.
Little wonder they struggled defensively, with Danny Welbeck exchanging passes with Lingard before firing an early chance straight at Ante Covic.
It was not long before the same pair were combining to score the first goal of Moyes' time in charge.
Showing imagination to dummy Ryan Giggs' pass, Welbeck allowed the ball to run on to an unmarked Lingard.
The 20-year-old kept his nerve to put the visitors in front from 10 yards.