Mark Wotte's side offered little resistance as Varney, whose loan spell has come to an end, hit the target in each half and squandered two opportunities.
Wednesday, who are safe in mid-table despite only one win from their last eight games, were handed a half chance when Francis Jeffers cut inside only to drag his low strike wide of the far post.
Struggling Southampton, desperate for three points, almost found a way through when Bradley Wright-Phillips fired across the face of the Wednesday goal as the incoming Jason Euell just failed to connect.
The Sheffield side should have gone ahead after Etienne Esajas picked out Sean McAllister on the left. His precise cross fell perfectly for on-loan Derby striker Varney but he side-footed his volley high over the bar.
Southampton had another let off as Varney's cross was turned round the foot of the post by Lloyd James as Jeffers was about to connect.
Wednesday went ahead in the 24th minute when centre-back Jan-Paul Saeijs was caught in possession by Jeffers.
He unselfishly fed Varney who ran through to coolly slot the ball beyond the exposed Kelvin Davis as he raced off his line.
Varney was guilty of another astonishing miss when he headed wide soon after from just six yards.
David McGoldrick headed over before Southampton were almost back on level terms minutes before the break.
Midfielder Rudi Skacel played the ball into the path of Euell, centre-back Richard Hinds partly blocked and Lee Grant pushed the ball round the foot of the post.
The Sheffield side had a let off when they failed to cut out Euell's cross from the right as McGoldrick drilled in a right-foot shot which flew over the top.
Wednesday killed off Southampton in the 73rd minute as Chris Perry and Saeijs both went for a throw in and failed to connect as Varney ran on to round Davis and slot the ball into an empty net.