Parkinson made two changes to the side that started Wrexham’s 2-0 triumph over Bristol City as Lewis O’Brien and Matty James replaced George Dobson and George Thomason.
Ismael made one change from his side’s 1-0 defeat by Queens Park Rangers as midfielder Adam Forshaw came in for Kristi Montgomery.
Wrexham edged the opening stages without troubling visiting goalkeeper Pears, but as they have done regularly on their travels this season, Rovers stunned the home crowd on the counter-attack.
Ryan Alebiosu had plenty of space on the right and his floated cross found Gudjohnsen who nodded beyond Arthur Okonkwo.
It served as a real blow for the hosts who went into the game having kept four successive league clean sheets and had not conceded first in any of their previous seven Championship fixtures.
Yuki Ohashi then failed to guide his speculative effort on target as the visitors continued to grow in confidence after taking the lead.
Wrexham’s only opening of the first half saw James McClean head Ryan Longman’s deep cross into the side netting – with Cleworth producing a vital block to ensure Ryoya Morishita’s shot did not trouble Okonkwo.
The hosts badly needed a spark in the second half, but they were fortunate not to go 2-0 down just before the hour mark as Dan Scarr’s loose pass was intercepted.
Ohashi was brilliantly denied by Okonkwo after being played through on goal by Taylor Gardner-Hickman, with Gudjohnsen firing the rebound over from close range.
Parkinson sent on Callum Doyle, Josh Windass and Dobson for Scarr, O’Brien and Ben Sheaf in the 59th minute as the Welsh side sought any kind of attacking momentum.
Kieffer Moore fired an acrobatic effort well wide, before George Pratt cleared another effort from the Wales international away from danger as the hosts ramped up the pressure.
Blackburn very nearly doubled their lead on 70 minutes in fortunate circumstances though, as substitute Makhtar Gueye’s cross deflected off Cleworth and inches wide of Okonkwo’s post.
Wrexham registered their first effort on target in the 84th minute as goalkeeper Pears denied Moore from point-blank range – with Cleworth’s follow-up effort hitting the crossbar.
Moore then crossed for Broadhead who could only guide his effort wide, but Cleworth got a vital touch on Broadhead’s last-gasp effort as the hosts snatched a point.
