Ross and Lehmann (50 from 74 balls) rescued the Redbacks from a sluggish start after the home side was reduced to 3/8 inside the first two overs.
Right-hander Ross battled bravely after copping a nasty blow to his hand early in his innings to carry South Australia to 9/228 in the State’s first home one-day match in more than six years.
But Tigers opener Ben McDermott ensured his side would record its maiden win of the tournament, carving out a mature century to ease Tasmania to the target total with more than three overs to spare.
McDermott, last season's One-Day Cup Player of the Tournament, hit his second one-day ton and finished unbeaten on 103 in a 140-ball innings.
His opening partnership with Caleb Jewell put on 132 for the first wicket to extinguish any real chance of a Redbacks’ run at victory.
SA claimed three wickets late in the piece to build some pressure on the Tigers’ middle order, but it proved only a momentary delay to the final result.
Cameron Valente, Lloyd Pope, returning captain Travis Head and leg-spinner Adam Zampa, who also affected a run out, finished with a wicket apiece for the home side.
The two teams meet again on Tuesday at Karen Rolton Oval.
Thanks to everyone who joined us at Karen Rolton Oval today 😊— West End Redbacks (@WestEndRedbacks) September 29, 2019
Disappointed we couldn't get the result for you, but we loved the fun, family atmosphere on a big day for our State ❤🖤 #MarshCup pic.twitter.com/isJ9IuLEPl