Preston got off to a bad start when Dickson Etuhu was stretchered off after one minute holding his left leg. He was replaced by Michael Keane.
Mark Kinsella had a shot saved by Andy Lonergan and David Healy had two corners that Russell Hoult firstly punched and then caught before Kinsella had another chip saved by the Preston keeper.
Andy Johnson fouled Ricardo Fuller on the edge of the penalty box and Graham Alexander took a quick free kick, tapping the ball to Eddie Lewis.
His 20-yard left-foot drive into the top left-hand corner of the net to made it 1-0 after 32 minutes.
Johnson then took a left-wing corner which Thomas Gaardsoe met with a powerful header but Lonergan made a great save and tipped the ball over the bar after 51 minutes.
Gary Megson, the West Brom boss, made a double substitution after 63 minutes, withdrawing Neil Clement and Kinsella and bringing on Jason Koumas and Lloyd Dyer and ten minutes later Lee Hughes was substituted by Morten Skoubo.
Preston made it 2-0 after 75 minutes when Fuller, in a central position, played the ball out to David Healy and he took the ball into the penalty box and hit a ten-yard shot which deflected off Hoult into the bottom right-hand corner of the net.
Healy was booked for celebrating by referee Mr Winter and Michael Keane forced a great save from Hoult when he was clean through and the keeper saved for a left-wing corner.
Lonergan made another great save with six minutes to go when a Darren Moore header from a Koumas corner was saved.
Rob Edwards came on for Lewis with five minutes to go and Gaardsoe was adjudged to have handled the ball for a penalty with four minutes to go which Alexander hit right-footed into the bottom right-hand corner of the net.