The result means Ethiopia, with an unassailable five point lead with one qualifying match remaining, automatically finish top of Group A and progress to the final round of World Cup qualifier playoffs.
With the scores locked at 1-1 with goals from Getaneh Kebede and Parker, a stunning own goal determined the outcome in the 70th minute. Parker on this occasion put the ball in his own net in an attempted clearance from an Ethiopian free-kick.
The top team in each of the 10 African groups will go through to the third round, where they will play home-and-away playoffs for the five World Cup spots up for grabs.
Earlier, a nervy start for Bafana forced goalkeeper Itumeleng Khune into making a solid stop as early as the third minute after Ethiopia's Saladin Said knocked a dangerous ball goalwards from a set-piece on the edge of the area.
Thuso Phala replied in the 11th minute with Bafana's first opportunity after Khune turned defence into attack, which allowed Phala space and time to shoot, but failed to test Jemal Tassew in goal.
Ethiopia piled on the pressure as the opening half approached the midway mark, but Khune was equal to the task, denying Said in the 16th minute, before Parker forced a good stop from Tassew two minutes later as the encounter started to open up.
The visitors asked questions of the Ethiopia defence on the half-hour mark, when Parker's headed effort was cleared off the line from a Phala corner.
Parker would not be denied two minutes later, when he picked up an accurate ball from Khune, before striking the dipping ball first time and beating Tassew at the far post to make it 1-0 to Bafana.
But a defensive lapse three minutes from the interval allowed Ethiopia to equalise through Getaneh Kebede, who benefited from some sloppy defending, beating Khune with a clinical finish, to level the game for the hosts shortly after conceding.
Following a Bafana free-kick, just outside the box, driven into the wall in the 63rd minute, Tshabalala crossed for Eric Mathoho who tussled with Tassew and headed the ball but was unable to keep the shot down.
Tlou Segolela came in for May Mahlangu in the 66th minute as Igesund hoped to introduce more pace to Bafana's attacks.
An incredible own goal gave Ethiopa a 2-1 lead with 20 minutes remaining. From a free kick an attempted clearance went awry as Parker only managed to head the ball perfectly into the top corner of the net.
Bafana's final qualifying match will be at home against Botswana on September 6. – Sapa