However, yellow cards for Luke Charteris and Ospreys' fly-half Dan Biggar allowed South Africa back into the match.
Scarlets hooker Ken Owens scored to extend Wales' lead but Willie Le Roux's try put the Springboks within striking distance.
And the hosts were awarded a penalty try in the dying moments of the match following a shoulder charge from Liam Williams into Cornal Hendricks.
Morne Steyn was on hand to convert, handing South Africa a 31-30 win and condemn Wales to their 24th defeat in 25 games against the Southern Hemisphere's big three under coach Warren Gatland.
However, despite the loss, Jones believes his side's performance is an indication as to what Wales are capable of producing on the biggest stage.
"We are 15 to 16 months out from the World Cup, hopefully, this will send a bit of a flare up into the sky to say we are still here and hopefully we can be contenders," said Jones.
"We wanted to show fans we are not out here on a jolly. We wanted to put in a good performance."
Elsewhere, Scotland came back from nine points down with ten minutes to go to claim victory over Argentina.
Tries from Glasgow Warriors' stars Stuart Hogg and Henry Pyrgos and three penalties from Duncan Weir was enough to see off the threat of the Argentines.
And Italy were edged out in a nail-biting encounter with Japan who picked up a 26-23 win in Tokyo.
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