Chaplow hit an unstoppable 20-yard shot into the bottom corner to make it 2-0 to Preston after 33 minutes, after Stoke's Ryan Shawcross had fouled Karl Hawley to concede a free-kick.
Goals from Chris McCann and Steven Caldwell pushed Burnley back to within two points of the Championship play-off zone with a 2-0 victory over Coventry.
McCann took his tally to the season for five with a 20th minute drive, while Caldwell's late header was his first for the Clarets since signing in January 2007.
McCann seized his opportunity when the Sky Blues defence failed to deal with Wade Elliott's 20th minute corner.
However, there was a hint of controversy in the build-up as Kyle Lafferty appeared to handle the ball inside the area.
But referee Tony Bates ignored the appeals and Leon Best could only add to their frustration as he had an effort ruled out for offside six minutes later.
Barnsley and QPR played out a dull goalless draw at Oakwell.