This was a first league meeting of these two clubs since a third-tier encounter in 2002.
The scrap to be Wales' top side – which also involves Swansea City - will be an interesting a subplot in the Championship this season.
Wrexham begin the campaign with the greatest expectations, and have enough experience and depth in their squad to suggest that a second successive play-off push is a realistic target for a club whose ultimate goal is to reach the top flight for the first time.
The options at Parkinson's disposal might make Brian Barry-Murphy a little envious, though Cardiff head coach is unlikely to say as much.
Cardiff look light on numbers – and Championship know-how – in comparison to their north Wales rivals, but that did not stop them finding a way to avoid defeat after the shock of conceding inside three minutes when Moore galloped on to Danny Imray's ball over the top and steered home first time.
Moore's fifth strike in five appearances against Cardiff since he left the Welsh capital for Bournemouth in 2022 seemed set to settle a contest in which Wrexham carried the greater threat for long spells.
As well as hitting the woodwork twice, Wrexham were twice denied by Cardiff goalkeeper Nathan Trott as he kept out efforts from Doyle and Imray, who shone on his league debut following a summer move from Crystal Palace.
Cardiff did have their moments, with Jack Moylan – the one new face in Barry-Murphy's squad – lifting an effort over the top and Cian Ashford shooting too close to Patterson.
But Wrexham were guilty of failing to capitalise on the game's clearest sights of goal - and paid the price when Rubin Colwill brought the house down in the last act of the game.