Williams won the Bank of the West Classic with a straight-set win over Coco Vandeweghe and remains No. 4 in the rankings while Errani, the world No. 9, took the Italiacom Open, beating Barbora Zahlavova Strycova in the title match.
The updated rankings Monday saw no changes in the Top 10 but Zahlavova Strycova moves from 71 to No. 60 and Vandeweghe flies up 51 spots to No. 69.
Victoria Azarenka's second stint at the top of the rankings has pulled her into a tie with Tracy Austin and Maria Sharapova for 12th most number of weeks at No. 1. They have been ranked first for 21 weeks. At No. 11 on the list is Dinara Safina with 26 weeks and Amelie Mauresmo is 10th at 39.
Azarenka has 8,800 ranking points, 270 more than world No. 2 Agnieszka Radwanska with Sharapova in third at 8,370 and Williams fourth with 7,830.
Errani is the top seed at the Sony Swedish Open and Bartoli is first in the field at the Mercury Insurance Open in California in this week's WTA tournaments.