Wednesday, still smarting from last week's 4-1 defeat at Wolves, carved out the early chances, Sean McAllister firing over from the edge of the area before Marcus Tudgay weaved into the area, his low left-foot strike spinning the wrong side of the far post.
They snatched the lead in the 20th minute, full-back Tommy Spurr caused havoc with a long throw, keeper Andy Lonergan failed to clear and McAllister hooked the ball into the net from 15 yards.
Wednesday dominated but were unable to increase the lead, the lively Etienne Esajas picking out James O' Connor who cut inside, his right-foot shot taking a deflection.
Preston, forced back by the pace of Esajas and Jermaine Johnson were disappointing, their first real chance coming in the 26th minute, Chaplow's fierce strike flashing wide of the target.
Wednesday almost grabbed a second five minutes after the restart, Esajas' cross from the left was met by Deon Burton whose powerful header hit Chris Sedgwick as he guarded the line.
Preston picked up the pace, Spurr throwing himself at the ball to block a Billy Jones strike before producing a carbon copy stop to keep out Sedgwick.
Chaplow should have equalised in the 75th minute after Sedgwick picked him out but he curled his close-range shot wide of the far post.
The same combination conjured Preston's goal two minutes later, substitute Ross Wallace picked out Sedgwick, he passed inside to Chaplow, who finished off from three yards.