The striker, who joined from Monaco last week, opened his account for his new side as Mapou Yanga-Mbiwa, Adam Armstrong and fellow new-boy Siem de Jong also scored
The French striker moved to St James' Park from Monaco last week and was handed his debut by Alan Pardew for the first game of Newcastle's tour of New Zealand.
Having been beaten by Oldham Athletic in their first pre-season outing, Siem de Jong got Newcastle off to an ideal start with an early opener.
He took advantage of an Ivan Necevski error before Riviere opened his Newcastle account with Mapou Yanga-Mbiwa getting in on the act before the break.
Both sides made plenty of changes at the interval and in the second half, with chances few and far between as a result. There was time, however, for Adam Armstrong to add a fourth and cap a comfortable outing for his side.
Having started brightly, Massadio Haidara and Rolando Aarons looked lively as they both whipped in dangerous crosses that came to nothing.
After 19 minutes Newcastle were handed a gift by Sydney goalkeeper Necevski who dawdled on a simple back pass and allowed Riviere to take possession.
He coolly played it to De Jong, who sidefooted home to score for a second consecutive game before the Premier League side doubled their lead seven minutes later.
Yoan Gouffran was the architect as he crossed for Riviere to register his first goal for the club and the goals continued as Yanga-Mbiwa's deflected strike beat Necevski all ends up.
Having coasted to a 3-0 lead at the break, Pardew opted to withdraw De Jong at half-time and Riviere early in the second period.
Corey Gameiro then went close with a curled effort just after the hour on a rare burst forward for the Australian side.
While it looked as though the A-League outfit would shut Newcastle out in the second half, their superior cutting edge proved the difference as Armstrong prodded home from inside the area late on.