Neither side threatened early on as Arthur Okonkwo did well to ensure Brad Potts – making his first start of the campaign – was unable to round off a slick move from the visitors.
But an uneventful contest came to life after Josh Windass’ deflected strike looped over the crossbar.
Daniel Iversen denied Broadhead and Kieffer Moore in quick succession before Mads Frokjaer-Jensen fired straight at Okonkwo at the other end.
The majority of the 10,616-strong crowd thought the hosts had gone ahead just before the half-hour mark when Okonkwo’s quick throw set Broadhead free, but Wrexham’s record signing could only drive an effort wide after a mesmerising run from the halfway line.
But Broadhead was clinical six minutes before the interval as Moore crossed from the right to pick out his fellow Wales international who guided his header into the bottom corner of Iversen’s net.
Wrexham were dealt a blow in the final seconds of the opening half as top-scorer Moore was forced off through injury, with Sam Smith replacing the towering frontman at the break.
The Lilywhites improved after the restart as Thierry Small tested Okonkwo with a driven shot, although Windass curled wide soon after with Wrexham growing increasingly reliant on counter-attacks.
Paul Heckingbottom’s side spurned a glorious chance to make it 1-1 on the hour mark as Devine could only volley into the side netting after being left unmarked from Ben Whiteman’s corner.
Iversen had to be alert to palm substitute Smith’s thumping hit wide – with Callum Doyle missing the target with a header from the resulting corner.
Parkinson’s side were inches away from doubling their lead on 74 minutes as George Thomason’s looping cross was headed against the post by Smith.
But two substitutes combined as Wrexham made it 2-0 when George Dobson split the Preston defence before Rathbone coolly slotted beyond Iversen 13 minutes from time.
Devine set up a tense finish as he fired into the bottom corner but, despite a nervy finale, Wrexham held on for an eighth league win of the season to inflict just a fifth Championship defeat on Preston in 2025-26.