Wrexham now sit two points above the third-placed Chairboys with two matches remaining of the regular season.
Blackpool – who had won six of their previous eight games prior to facing Wrexham – are nine points adrift of sixth-placed Leyton Orient in 10th with just three games left to play.
The visitors edged the opening stages as Rathbone tested Harry Tyrer, although clear cut chances were few and far between early on.
Wrexham co-owner Rob McElhenney was among the 2,000 or so supporters in the away end at Bloomfield Road.
And the It’s Always Sunny in Philadelphia actor could be forgiven for wondering how he and those fans around him were not celebrating in the first half as Parkinson’s men turned the screw.
Former Republic of Ireland international McClean appeared destined to open the scoring as he cut in from the left before firing goalwards, only to be denied by a stunning Tyrer save.
The goalkeeper then produced a fine reflex save to keep out Jay Rodriguez’s strike, although Arthur Okonkwo tipped over a Apter shot at the other end as the score remained level at the break.