After losing the toss and being sent in to bat, Tasmania went to stumps on day one at a dominant 5-335, with Brad Hope (83no off 145 balls) and Jake Doran (69no off 99 balls) in complete control.
Maddinson, suiting up for the first time since being dropped for Australia's deciding Test against the Proteas in South Africa, pulled off a spectacular diving effort at square leg to dismiss dangerman Mitch Owen for a first-ball duck on Friday.
But steadying knocks from former WA batter Teague Wyllie (64) and Caleb Jewell (46) swung momentum back Tasmania's way, before Hope and Doran piled on the pain.
Maddinson, who bowls part-time spin, was the seventh bowler NSW turned to in an attempt to break down Tasmania's batting line-up, but he was only able to return figures of 0-31 from eight overs.
The 34-year-old will have the chance on day two to strut his stuff where he feels most comfortable - at the batting crease.
Maddinson received a shock Test call-up for the series in South Africa, but apart from his brisk 48 in the second innings in Durban, his other three scores of 0, 0 and 8 meant the writing was on the wall ahead of the deciding third Test.
NSW will need him to be firing all cylinders given Tasmania are well set to post a first-innings total that could give 500 a nudge.
Doran and Hope's unbeaten partnership currently stands at 153, with the pair combining for 22 boundaries as the NSW attack tired.
Jake Scott (2-66) had the most luck, the paceman snaring the edge of Jewell before dismissing Wyllie caught and bowled.
Wyllie threw his head back in disbelief after popping the easy return catch to Scott.
And when Sean Abbott (1-37) trapped Jordan Silk in front for 37, Tasmania were looking shaky at 5-182.
But Doran and Hope took the game away from NSW, seeing out the rest of the day to put Tasmania into a position of strength.
