British number one Konta, who reached the semi-finals of the Australian Open this year, served eight aces on the way to knocking out the Swedish qualifier.
The 24-year-old will face Italy's Roberta Vinci in the next round.
In the men's event, Slovenia-born British number two Aljaz Bedene lost 7-6 (7-3) 7-6 (10-8) to France's Stephane Robert.
Fellow Briton Heather Watson had already made it through to the second round in Rome with a win over world number 18 Sara Errani on Monday.
Konta is ready to face a vociferous home crowd when she takes on 2015 US Open finalist and home favourite Vinci, with the match likely to be on a stadium court.
"She's a great player, incredibly talented and creative," Konta told BBC Sport.
"I hope to bring a good level to the court and the fans will be able to enjoy it.
"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."
Britain's Johanna Konta reached the Italian Open second round with a 6-1 6-2 win over Sweden's Johanna Larsson.