The British No.1, who reached the Australian Open semi-finals this year, served eight aces as she beat Sweden’s Johanna Larsson 6-1, 6-2 in round one.
She will now face 2015 US Open finalist Vinci in the second round and Konta is under no illusions about the challenge the Italian poses.
"She's a great player, incredibly talented and creative," said Konta. "I hope to bring a good level to the court and the fans will be able to enjoy it.
Williams wins first title in nine months in Rome
"Whoever the fans will be cheering for - and it will most likely be her - it'll be just great to attract a lot of people and the energy they bring. It's definitely a pleasure to play in front of big crowds."
Williams sets up all-American Rome final with Keys
Serena, Konta through in Rome