Redbacks captain Travis Head won the toss at Glenelg with Worrall claiming his first scalp in the opening over of the match.
Worrall struck again in his second over and finished with impressive figures of 5-72 for his fifth first-class five-wicket haul.
Joe Mennie took his 200th Shield scalp for SA after skipper Head held on to a difficult chance to end Hilton Cartwright’s innings.
The Warriors rallied after the early onslaught from 4-63 to be eventually all out for 355 in an evenly-matched contest.
The visitors counter-attacked with some aggressive batting, led by skipper Ashton Turner, who brought up his 50 at better than a run a ball before eventually falling for 79 off 89 deliveries.
Cartwright scored a more-measured 83, while wicketkeeper Josh Inglis added 86 in entertaining fashion.
Redbacks openers Jake Weatherald and Conor McInerney were forced to survive a single over before stumps, safely reaching 0-4.