Opener O’Neil posted her highest score of the 2019-20 season with 90 from 117 deliveries, before being run out.
Stacey Oates added 24 runs to the Blues’ total, while tail-ender Beth Worthley contributed with an unbeaten 18.
Chasing 188, the Browns struggled after the early loss of star batter Bridget Patterson (1), with Rachel Church putting on the most runs with 21.
Kensington’s batting order collapsed, thanks to Price’s 5/12 and Brooke Harris’ 3/19, with the Browns all out for just 67.
Earlier, Shae Daly was the standout for Kensington, taking three scalps.
Tahlia McGrath (53) led with the bat for West Torrens in their match against Northern Districts, while Angela Treloar (19) and Kayla McGrath (18) provided support.
Two wickets each to Sam Betts, Neisha Iles and Emma Faint had the Eagles dismissed for 160 in the 49th over.
The Jets chased well, with Tegan McPharlin (26) and Mary Waldron (46) putting on a 42-run first-wicket stand.
Iles (20 not out) assisted well and Northern Districts reached 7/161 with more than six overs to spare.