The offspinner posted 146 from 165 balls, compiling the second century of her First Grade career and highest total at this level.
Southern District was missing a number of key players who were competing at the Toyota Australia Cricket Country Championships, including captain Jess O’Reilly.
Price was supported by Annie O’Neil (48) and Rhianna Peate (67), with Sturt compiling a total of 5/280 after their 50 overs.
In reply, an inexperienced batting lineup struggled against the Sturt attack and were dismissed for 56, with Stacey Oates taking an incredible 6/14 from eight overs.
Bridget Patterson’s unbeaten 58 for Kensington led her side to a comprehensive victory over West Torrens, who were dismissed for 105 inside 32 overs.
Ellie Falconer (42) and Laura Niejalke (25) top-scored for West Torrens, however no other batters got going, thanks largely to Kensington’s Sarah Lowe (3/10) and Sarah Ferris (3/16) taking three wickets each.
The Browns reached 4/109 in 18 overs and maintained their place atop the ladder after six rounds.