The Lilywhites goals came from Daley and Clark with a brace from Rob Oselby and a goal from Adrian Cieslewicz netting for Wrexham.
Wrexham had previously had only won one with four draws and two defeats in their previous seven matches.
Preston had included two trialists with Championship experience, Hungarian Gabor Gyepes and Serbian Goran Loure who had previously played for Cardiff and Barnsley respectively.
Burnley now lead the table by one point after nine matches with North End second and Morecambe third.