The Lancashire side had snatched the lead after a blunder in the Wednesday defence, before Preston keeper Andy Lonergan gifted the Sheffield side a goal minutes after the restart, with Jeffers having the final word.
Wednesday, whose disastrous run of six games without a win has plunged them into deep trouble, were handed an early chance after centre-back Liam Chilvers nudged his opposite number Richard Hinds on the edge of the area.
Burton O'Brien produced a curling free kick, the ball taking a slight deflection as it spun over the target, before Deon Burton set up Hinds whose low strike from 20 yards curled wide of the far post.
Simon Whaley almost found a way through minutes later hitting a spectacular right-foot strike from 25 yards tipped over the bar by the alert Lonergan.
The Sheffield side escaped, veteran defender Lee Bullen clearing a teasing Whaley cross at the far post, but the Preston midfielder did better minutes later picking out Lewis Neal, whose tame header was snapped up by the Wednesday keeper.
Bullen was the villain in the 35th minute as Preston snatched the lead, his miscued backpass letting in Karl Hawley, who coolly rounded Lee Grant to slot the ball into the empty net.
Under pressure, Wednesday escaped minutes before the break Grant first to the ball ahead of Chilvers and Darren Carter, after his defenders had failed to cut out a Neal cross from the left.
Wednesday were back on level terms in the 51st minute after Lonergan's blunder, O'Brien's hopeful ball upfield bounced in front of the Preston keeper as he came out to clear on the edge of his area and as it looped over him Akpo Sodje nipped in to stab the ball over the line.
Jeffers hit the winner in the 82nd minute, full-back Matthew Hill handling after Marcus Tudgay spun quickly in the area, to allow the ex-Blackburn striker to drill his spot-kick past Lonergan.