The 20-year-old became a firm favourite when he smashed in seven goals in as many games during his loan spell with Wednesday last season.
His goals were enough to ensure a play-off spot before he returned to the South Coast and Wednesday went on to promotion.
Meanwhile Saints – who fired Sturrock a year ago following a brief five-month spell as manager – dropped out of the Premiership.
And Jones has already begun to repay Harry Redknapp's faith in him with two goals in two games as Southampton try and find their feet in the lower division.
Wednesday, with a point apiece from their first two games, showed no fear against the former Premiership side.
Just two minutes in Chris Brunt set the tone with an impressive cross from the left which was headed just wide.
New striker David Graham, a £350,000 capture from Wigan during the week, slipped a neat ball out to Brunt and the winger's stinging low shot was wide.
Wednesday keeper David Lucas had hardly seen any action as Southampton squandered a string of corners.
The best opportunity came when Djamel Belmadi made a slick break down the left and put Wednesday on the back foot but Darren Powell smashed an optimistic shot high over the bar.
But the opening goal came the way of the South Coast side in bizarre fashion after 22 minutes.
Wednesday defender Richard Wood tried to control a simple ball on the edge of the penalty area but slipped and fell on his back scuffing it only a few yards.
Jones darted in to intercept and as Frank Simek tried to force him wide the Trinidad international kept his cool and fired a low shot beyond Lucas.
It rocked Wednesday but the home side continued to carve out their chances and Brunt threatened with a spectacular 25-yard effort that drifted off target after Chris Eagles slid the ball to him from a free-kick.
In the second half Southampton, with the one-goal cushion, eased into control and the two divisions that separated these sides last season reopened.
A neat passing move opened up Wednesday again and released Dexter Blackstock only for Simek to produce a tremendous tackle as he threatened to extend the lead.
And Lucas was forced to produce his best save of the afternoon when Jones picked out midfielder Matt Oakley who hit a piercing low shot that the goalkeeper held diving low to his right.
Substitute Adam Proudlock might have leveled after Brunt swung in a textbook cross, but as the Wednesday striker poised for the header, the alert Powell intercepted.