The World Sevens Player of the Year nominee also struck twice in the 21-14 cup quarter-final defeat against Fiji, which was settled when Jamilai Naikadawa struck in the final move of the match.
Tom Powell and Sam Edgerley then got the scoreboard moving against the Blitzbokke only for England to find themselves trailing 17-12 in the final moments and pinned on their own line.
But Edgerley twisted his way out of trouble and Turner shrugged off a tackle before accelerating 70 metres to the line with Tom Mitchell's conversion completing the escape act.
Earlier, New Zealand duly clinched their 10th HSBC Sevens World Series title by beating South Africa 36-0.
Elsewhere Wales recovered from Saturday's shock defeat at the hands of Spain to beat the United States 28-19 with Richard Smith, Adam Thomas, Craig Price and Alex Walker all scoring.
They then sidestepped another surprise result when Dan Fish's two tries ensured a 28-26 win over Portugal with Walker and Rhys Patchel also scoring.
Scotland logged a 21-5 win over Kenya with tries from Michael Fedo, Bryon McGuigan and Andrew Skeen, then advanced to the Bowl final with a 31-19 win against Zimbabwe. Fedo scored twice with McGuigan, James Fleming and Andrew Turnbull adding further tries.
On day one, England had beaten France 28-0 and the USA 15-5 before a 14-7 defeat to Samoa halted their progress.
Against Fiji - who will finish the series in second place - they produced their most incisive attacking work of the weekend.
They trailed to Setefano Cakau's early try but a composed build-up with good work from Edgerley and Chris Cracknell put Turner away with Mitchell converting.
They hit the front in the second half with Dan Norton involved on the left before Turner was put away down the middle for a 14-7 lead.
Fiji levelled two minutes from time through Isake Katonibau but England dominated the closing moments with Turner and Rob Vickerman bursting into the Fiji 22 before the islanders got out of jail.
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