At Edgbaston, Warwickshire were 69-5 in the 11th over but Dutch batter Sterre Kallis held the innings together with six boundaries in making 38 from 30 balls.
Millie Taylor, who scored an unbeaten 26 from 27 from number eight, was the only other significant score as the Bears, who stay third following their defeat, were bowled out for 139 with three balls unused.
Jones, with her first half-century of the season, and the lower order then did enough for Surrey’s eighth victory in 10 games to push them six points clear at the top.