Williams and Robinson crossed within three minutes of each other and Parks botoed two penalties and converted both tries.
Cardiff took the lead after 15 minutes through a Parks penalty before De Waal levelled with a kick of his own.
Cardiff were back in front when Richie Rees broke through the middle and fed Martyn Williams who sprinted over in the corner, Parks adding the difficult conversion.
Parks then intercepted and fed Robinson who also sprinted in at the corner to give the visitors a 17-3 half-time lead.
A Parks penalty early in the second half extended Cardiff's lead before the home side piled on the pressure.
A driving set-piece five metres out rewarded Treviso as Picone touched down.
Brendan Williams added a second try for the home side shortly after which secured a losing bonus point for Treviso.
Munster climbed to second in the RaboDirect Pro12 table after securing a 24-14 win over Newport Gwent Dragons at Rodney Parade.
The Irish province leapt over the Ospreys and stretched away from the chasing pack in the race for the play-offs thanks to a late surge in Newport.
The visitors scored 15 points in the last 12 minutes to secure the win and ensure the Dragons did not get a losing bonus point for their efforts.
Munster, without a sizeable international contingent, settled quickly and opened the scoring with a third-minute penalty from fly-half Ian Keatley.
But the Dragons worked their way into the game and deservedly levelled the scoring thanks to a penalty from opposite number Lewis Robling on 17 minutes.
The hosts were soon in front when a marvellous 50-metre jinking run by full-back Will Harries allowed centre Ashley Smith to dive over to make it 8-3.
However, the conversion was wide and it was the Irish visitors that soon got their noses back in front thanks to a pair of Keatley penalties.
Back came the Dragons and Robling knocked over another penalty to edge the hosts in front in an error-strewn encounter, an 11-9 lead that they held at the break.
The hosts were having the better of things in possession and territory but were unable to break clear of a resilient Munster side.
The Dragons suffered a blow when centre Andy Tuilagi limped off the field and was replaced by 17-year-old Jack Dixon, who last year became the youngest player to turn out in Welsh regional rugby in the LV= Cup win against Wasps.
And the teenager nearly had a dream introduction to the Pro12 when he featured prominently in a dashing 60-metre move that was ended agonisingly close to the line.
Once again Munster had escaped, but they were under severe pressure when scrum-half Tomas O'Leary was sin-binned on 58 minutes after referee Carlo Damasco got fed up with the visitors infringing at the breakdown.
The Dragons kicked a penalty to the corner and laid siege to the Irish province's line.
Munster defended heroically and next time the Dragons earned a penalty they went for the posts with Robling successfully making it 14-9 with 15 minutes remaining.
However, it was not a lead that they held for long. Replacement Denis Hurley went flying through a gaping hole in midfield and the ball was worked wide from the next phase for fellow wing Luke O'Dea to dash over down the right.
Replacement fly-half Scott Deasy missed the conversion but was accurate minutes later when presented with a 40-metre penalty to put the visitors 17-14 up with 72 minutes on the clock.
And it was game over with five minutes left when full-back Felix Jones snaffled a loose ball in midfield to race over under the posts, Deasy adding the routine extras for a hard-earned win.