Opting to bat first, NSW made a mediocre 9-178 at Sydney's Bankstown Oval before dismissing Tasmania for 97 in 35 overs to claim a bonus point.
Smith (70 off 99 balls) held the Blues innings together, striking four boundaries and two sixes in a responsible innings on a slow wicket.
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He came in at first drop, after Test opener David Warner (4 off 16) was caught at second slip in the fourth over.
The Tigers were reasonably placed at 1-51 in the 16th over, but their challenge crumbled as they lost 4-6 in just over six overs.
A combination of disciplined bowling, poor running and fine catching turned the match around.
Cosgrove was snapped up at point by Warner, while Bailey fell victim to a sharp return catch from emerging paceman Gurinder Sandhu (1-15 off six overs).
When Ed Cowan (25 off 50) perished off the last ball of the 22nd over, Tassie were 5-57 and effectively out of the contest.
Earlier, Smith and Henriques (35 off 46), added 46 for the second wicket, before NSW suffered a mid-innings collapse, losing 4-21 to slump to 5-81 after 24 overs.
Smith and one-day debutant Kurtis Patterson (22 off 44) put on 53 for the sixth wicket, but the Blues added just 24 off the last 7.5 overs after Smith was bowled around his legs by Xavier Doherty (1-40 off 10).
Medium pacer Ben Laughlin (3-23 off 10) smashed through the bottom half of the order.