Errani was a semifinalist in last week's Mutua Madrid Open and gains enough rankings points to move to No. 6, passing Angelique Kerber. Errani, along with teammate Roberta Vinci, is No. 1 in the WTA's doubles rankings.
Wozniacki swaps places with Samantha Stosur for ninth in the rankings, relegating Stosur to 10th. Both lost in the first round of the Madrid Open.
But Williams, with four championships in 2013, is No. 1 for a 13th consecutive week and 136 weeks overall. She had 11,115 points while Sharapova has 10,690 for the No. 2 ranking. Sharapova is the defending champion at this week's Rome International.
Errani has 5,640 points, 110 more than Kerber. Petra Kvitova remains eighth with 5,225 points. Wozniacki has 3,625 points and Stosur totals 3,545.
The entire Top 10 is in the field for the Rome tournament, a key event ahead of the French Open, which begins May 26.