In a scrappy opening period, Jermaine Johnson saw a curling effort fly narrowly wide while full-back Reda Johnson nearly caught out Preston goalkeeper Thorsten Stuckmann with an over-hit cross that landed on the roof of the net.
Paul Parry had North End's best chance of the first half but his tame free-kick was easily gathered by Stephen Bywater before Stuckmann turned over a drive from midfielder Johnson on the stroke of half-time.
Wednesday did not have to wait long for another chance and four minutes after the restart Chris Lines played in Madine and the striker spun to fire his 16th goal of the season into the top right-hand corner.
And Madine doubled his side's lead after 64 minutes, heading in Antonio's long throw from the right.
The striker spurned a couple of chances to claim his hat-trick in the closing stages while Preston offered little going forward as they slipped to a fourth game without a win.