Moscow-born Kazakh Rybakina got off to an edgy start in the rain-delayed contest by dropping her opening service game before the Wimbledon champion levelled at 3-3 and then wrapped up the opening set with a late break.
Kalinina, playing in the second singles final of her career, called the trainer on to the court after losing the opening game of the second set before quitting the match in tears.
Victory ensured Australian Open runner-up Rybakina won her second title of the year following her Indian Wells triumph and fifth overall.
She won three of her matches in Rome after her opponents retired and will now break into the top five on Monday.
She also reached the final in Miami and heads to Roland Garros as a top contender for the year's second major.