In front of a small crowd on Tuesday evening – just under 10 000 – the South Africans produced a vastly different display to Friday's 1-0 loss at the hands of Brazil.
Bafana had a stranglehold on possession, and while their defence was firm, they created few chances.
Parker produced a clinical finish to put his side ahead early, and then scored his second in the 88th minute to seal the result.
In Gordon Igesund's second game in charge, the home side never looked like conceding and eased to victory.
Moeneeb Josephs was handed a rare start in the Bafana goal as Igesund chose to rest Itumeleng Khune after a good performance against Brazil.
Josephs, however, was a spectator for much of the encounter. He made his first good save in injury time, courtesy of a toothless visiting attack.
The hosts started the match with the lion's share of possession and dominated the visitors.
Bafana were rewarded with the opening goal in the seventh minute through a well-composed finish from Parker. He made a perfectly-timed run down the left and with just Nelson Logomale to beat in the Mozambique goal, he slotted the ball into the back of the net to give Bafana an early 1-0 lead.
Three minutes later and it was the turn of Siphiwe Tshabalala. After a bustling run down the left, instead of passing, he made his way to the edge of the box, but his shot was scuffed wide of the far post.
Less than 60 seconds later, after a rampant passage of play from Bafana that left the visiting defenders stretched, Reneilwe Letsholonyane reeled off a first-time shot from 25m out, which was tipped over by the keeper.
From the ensuing corner, skipper Bongani Khumalo was able to get in a free header, but his attempt was just wide.
In the first 20 minutes, Igesund's troops held onto the ball well through short accurate passes, something they had clearly worked on in training.
Thulani Serero showed good interplay with Siboniso Gaxa in the 24th minute, and the pair's one-touch football allowed Serero to find his way into the box before banging a shot from close range, which just shaved the post.
In their only meaningful sojourn into the Bafana area, Helder Pelembe had the first shot for the visitors in the 29th minute after a strong run down the right flank. His strike was wide of target.
Tshabalala, from a free kick in a dangerous position 30m out in the 41st minute, opted to try his luck. His curling cross saw Bongani Khumalo head the ball into the back of the net, but the referee disallowed the goal for an infringement in the box.
In the 66th minute, Tshabalala had the best chance to double the lead, but his shot from close range was well-saved by Logomale.
With two minutes remaining Parker doubled his tally for the evening. When left one-on-one with just the keeper to beat, he nailed the strike to round out the 2-0 win. – Sapa