In reply, Edwards led an early run-scoring rout and New South Wales cruised victory with a whopping 93 balls to spare which earned them a bonus point.
Edwards thumped 11 fours and four sixes in his aggressive 63-ball innings, dominating a 137-run partnership with fellow opener Daniel Hughes.
Hughes made a polished 58 from 71 balls having been involved in an usual incident early in his innings when he was given caught behind off Riley Meredith having been distracted by bowler's towel falling out as he ran in. The umpires conferred and ruled it a deal ball so Hughes survived.
Meredith was then unable to complete his second over, leaving the field after five deliveries.
Earlier, Tasmania's batters apart from Webster were collectively stifled by a disciplined NSW bowling line-up. Pacemen Edwards, Jackson Bird and Hayden Kerr were among the wickets while curtailing the run rate.
Bird, making his first appearance for NSW against his former team, was exceptional with the new ball as he had Caleb Jewell caught a first slip third ball and began with back-to-back maidens.
He also had Jake Weatherald caught behind in an opening spell than finish 7-2-17-1.
Tasmania plunged to 75 for 6 in the 27th over but Webster then found an ally in No. 9 Paddy Dooley, the pair putting on 90 runs for the seventh wicket. Webster struck six fours in his 80-ball knock and Dooley made 39 from 63 balls.