Cornwall won the toss and skittled the visitors for 155, with 9.3 overs left.
No Taradale batsmen soldiered on, despite four of them getting into the 20s.
Cornwall skipper Charley Crasborn took 5-31.
At Havelock North, NOBM got home by the skin of their teeth with an eight-run victory against Bayleys Real Estate Havelock North CC.
"It was a good batting perform on a classic Anderson Park deck, which stayed slow and low, so we took our time," NOBM captain Bevin Pollock said, after winning the toss before amassing 207-4 in 50 overs.
Havelock skipper Jared Priest was the pick of the bowlers, claiming 1-24 from 10 overs, including three maidens.
No5 Casey Rangi was not out 62 and No6 Brendan Quinn was unbeaten on 54.
"Casey and Brendan also performed with the ball," Pollock said, after the visitors restricted the villagers to 199-9, with Rangi, Quinn and Anoop Renuka-Prajad taking two scalps each - although Damien Scott was the most frugal in claiming 1-27, including two maidens, and Mason Baker not far off with 1-38.
Poolock said NOBM would have former Bracewell academy player Jack Ward of England in their side as a No3 batsman and opening or first-change bowler from this Saturday, when the 40-over returns, because the Pay Excellence Hawke's Bay senior men's representative side resume their Hawke Cup campaign. The Bay team played a friendly in Taupo yesterday.
At Nelson Park, Napier, NTOB made short work of Ruahine Motors Central Hawke's Bay, with a comfortable six-wicket victory.
The visitors won the toss but must have rued their decision to bat, after after their total had a supermarket grocery bill look about it, with all out for 96 in 37.3 overs.
All NTOB bowlers made contributions, although veteran Jeremy Kuru took 4-14 from 6.5 overs, while teenager Christian Leopard claimed 3-19 from just as many overs and two maidens to boot.
Josh Paerau (31 runs), Indika Senarathne 28 not out and captain Goerge Diack unbeaten on 16 helped eclipse the total in 20.3 overs.
"This year we want to go to the nationals. It was the first round against the second-best team in the comp so we had to stand up and we did," Diack said.
His men were digging deep week in, week out for the collective.