The Scotland international opened the scoring with a smartly-struck 40-metre penalty after Edinburgh were pinged for not rolling away.
The Blues enjoyed some decent territory but things really clicked for them in the 16th minute, with Parks making the break which led to a try for lock Bradley Davies.
Parks swung the ball back inside to the supporting Richie Rees, Ma'ama Molitika then surged forward before drawing the cover and passing for Davies to bound over for the score, which Parks comfortably converted.
Presented with an opportunity to hit back, Edinburgh full-back Chris Paterson was narrowly wide with a penalty attempt, and the buoyant Blues were soon celebrating their second try.
Full-back Chris Czekaj did well to pass out of the tackle to Xavier Rush whose clever chip and deft offload laid the ball on a plate for winger Tom James to cross the whitewash. Parks' conversion made it 17-0.
Edinburgh, who won 22-21 here last year, rallied in the minutes leading up to half-time, courtesy of three penalty successes from Paterson. They should have had a try or two, as Cardiff's try-line came under increasing pressure.
A timely turnover saw the Blues clear the danger, and they needed Parks to produce an interception when the Scottish side looked poised to score on the overlap.
There was another near miss when centre Ben Cairns was just held up short, and Parks sandwiched a penalty in between Paterson's kicks to hand Cardiff a 20-8 advantage for the break.
The Blues made a clinical start to the second half, immediately attacking the Edinburgh line. Their forwards used a lineout take from captain Paul Tito to drive forward and hooker Rhys Thomas touched down for try number three, converted by Parks.
The home pack muscled their way back into scoring range shortly afterwards, and big Tongan Molitika was hauled down within sight of the whitewash.
On the hour mark, Edinburgh closed the gap to 27-16 with their first try of the new season. Powerful winger Tim Visser applied the downward pressure after an excellent break from the industrious Cairns.
Another try looked on the cards as the visitors enjoyed a dominant spell, during which Blues winger James was sin-binned for hands in the ruck. Still, Cardiff got back in the scoring groove with a cracking team try.
Turnover ball saw them quickly shift from defence to attack, with Molitika and winger Richard Mustoe bringing play up towards the halfway line.
After some clever passing, the injection of pace came from Czekaj as he zipped in and out before play was moved left, and the supporting Davies supplied the try-scoring pass for centre Casey Laulala. Man-of-the-match Parks added the extras to maintain his 100% kicking return, with six out of six.
There was still time for Visser, the recently named Magners Young Player of the Year, to grab his second try in injury-time, squeezing over in the left corner after another strong burst from number 8 Netani Talei. But the Blues still ran out comfortable winners.
Pleased to send the majority of the 6,542-strong crowd home happy, Parks said: "It was very tiring because we were running the ball a great deal late on. However, it was an enjoyable start and we're delighted to have kicked off with a win."
Speaking afterwards, Edinburgh coach Rob Moffat admitted: "We didn't deserve to win the game. We were sloppy and we couldn't build pressure on Cardiff.
"With ten minutes to go, I thought if we scored it would be interesting, but overall we made too many mistakes."
|Cardiff Blues Score Card|
|Edinburgh Rugby Score Card|