Blues' summer recruit Parks wasted no time in making his mark where it mattered, kicking the first points of the game at the first opportunity in the seventh minute.
The Australian-born Scottish international played a pivotal role in the superb opening try, executing a neat one-two with half-back partner Rees before Ma'ama Molitika set Bradley Davies free 20 metres out. Parks added the conversion.
Full-back Chris Czekaj started the next scoring move with some clever footwork and deft distribution and wing Tom James finished it off.
But in between number eight Xavier Rush underlined his value to the Blues after deciding to remain with them rather than join Ulster in the off-season.
The New Zealander took Czekaj's pass and with his path to the line seemingly blocked, chipped and gathered before flicking a one-handed reverse pass for James to go over.
Parks converted and added a penalty two minutes from the break, having also thwarted Edinburgh's most promising move by intercepting lock Fraser McKenzie's pass.
But Paterson had the final word of the opening period, kicking his third penalty up to that stage to give Edinburgh some hope going into the second period.
However, that hope took a big knock three minutes after the break as home skipper Paul Tito claimed a line-out five metres from the visitors line.
Tito's pack responded with a power-drive to the line where hooker Rhys Thomas was awarded the touchdown and Parks converted.
Molitika was held up over the line as the Blues produced another surge and Edinburgh's defence held firm from the scrum that followed.
The Scottish side also showed their battling qualities as wing Tim Visser finished off a fine move for Paterson to convert.
But the Blues produced the try of the night to seal the bonus point with a length-of-the field wonder try in the 75th minute.
It began with scrum-half Rees latching on to a loose ball in his own 22 and after good contributions from Molitika and Tom Shanklin, Czekaj was freed and again used his footwork and footballing skills to keep the defence guessing.
The full-back found Parks on his shoulder and lock Davies was on hand on the left flank to pass back inside for Laulala to go over and Parks converted.
Visser went over for his second - confirmed by the video referee - and Paterson converted from the touchline.
Cardiff Blues: Czekaj; Mustoe, Laulala, Shanklin, James; Parks, Rees; Jenkins, Thomas, Andrews, B Davies, Tito, Molitika, M Williams, Rush. Replacements: Jones for Tito (46), Warburton for M Williams (69). Not Used: Blair, Sweeney, L Williams, R Williams, Hobbs, T Davies.
Edinburgh: Paterson; L Jones, Cairns, Grove, Visser; Godman, M Blair; Jacobsen, Ford, G Cross, MacKenzie, MacLeod, MacDonald, Grant, Talei. Replacements: Houston for Grove (55), D Blair for Godman (70), Laidlaw for M Blair (70), Traynor for Jacobsen (55), Kelly for Ford (70), Gilding for G Cross (61), Hamilton for MacKenzie (61), Newlands for MacDonald (36).
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