Returning from national duties, Abbott (3-25) and Dwarshuis (3-30) took four scalps in the first four overs as the Tigers were rolled for 118 in 20.3 overs.
Wednesday's final in Hobart was reduced to 22 overs a side, after persistent afternoon rain almost forced a washout.
Tasmania took regular wickets to keep their hopes alive during the chase, but they couldn't dislodge man-of-the-match Patterson who was unbeaten on 52 from 57 balls.
The score capped off a dominant one-day competition for Patterson, who finished the leading run scorer for the season with 565 runs at an average of 113.
He had a life when Jordan Silk put down a tough chance at point, after coming to the crease in the first over when Josh Philippe (four) fell.
NSW got past Tasmania's total at 6-119 with 11 balls remaining.
"I don't think it's quite sunk in yet to be honest. We were about 10 minutes more rain away from not even getting on the field," Patterson said.
"It's wild how the day panned out.
"The people who were allowed a phone in there (the change rooms) were looking at that radar like you wouldn't believe and trying to move the clouds with their hands.
"You get lucky sometimes."
Due to their higher position on the ladder, first-placed Tasmania would have lifted the trophy if the game was washed out.
Instead they found themselves at 3-9 in the second over after Dwarshuis had Caleb Jewell (zero) and Beau Webster (four) caught in the slips in the first five balls.
Dangerous big-hitter Mitchell Owen (five) fell to Abbott in the next over, with Tasmania collapsing further to 5-25 when Silk (four) was run out chasing a risky single.
Nikhil Chaudhary top scored with 31 from 24 balls at No.8 but was dismissed with two-and-a-bit overs left when he hit spinner Joel Davies straight to cover.
Veteran Matthew Wade was one of just four Tasmanians to get to double figures, but he was out for 15 caught on the boundary off Tanveer Sangha.
"It's pretty raw. It's really disappointing. We had such a good campaign," Silk said.
"It felt like a really good opportunity gone by. It probably hurts more when you're out of the (Sheffield) Shield race as well."
NSW only qualified for the final after getting a bonus-point win over Tasmania in the final regular season game to jump up into second place.
It is their first One-Day Cup title since 2020/21, while Tasmania haven't lifted the trophy since 2009/10.
