Errani, who lost five games in a singles match Saturday, locked up the best-of-five series with a 6-1, 6-1 decision over Alisa Kleybanova in 59 minutes.
The second reverse singles match was called off and Italy completed a 4-0 weekend with a 4-6, 6-2, 10-4 doubles win by Flavia Pennetta and Karin Knapp over Russians Margarita Gasparyan and Irina Khromacheva.
Roberta Vinci took a three-set decision over Alexandra Panova in the first match of the series Saturday and Errani's 6-4, 6-1 decision over Khromacheva had the Italians on the brink of the Fed Cup title.
Errani wasted little time in sewing up the series Sunday, taking also three-quarters of the points in the first set and two-thirds in the second. Errani saved both break points she faced while winning 80 percent of the points on serve. She finished off five of her 11 break opportunities.
Italy has won four Fed Cups, all since 2006. The Italians won back-to-back in 2010 and '11 and were second to Russia in 2007. Russia is 4-6 in Fed Cup final series, having lost two of the last three years.