Lepchenko, appearing in her first Fed Cup tournament, lost her first set to Vinci but charged back to post a 2-6, 6-4, 7-5 victory.
Earlier in the day, Sara Errani gave Italy a 1-0 lead by beating American Jamie Hampton 6-2, 6-1 in a match lasting just 62 minutes.
Sunday's reverse singles pit Lepchenko against Errani and Hampton against Vinci. Doubles play has Nastassja Burnett and Karin Knapp on the schedule for Italy, even though Errani and Vinci teamed up last month to win the Australian Open doubles competition.
Celebrity Couples of 2014 [PHOTOS]