World number six Rybakina, the reigning Wimbledon champion, was leading 6-4, 1-0 when Kalinina called it quits with a left thigh injury shortly after midnight in a final long-delayed by rain.
Rybakina, 23, is the first player to capture two WTA 1000 titles this season having already won the prestigious Indian Wells hard court tournament.
She was also runner-up at the Australian Open and in Miami.
Rybakina, who will rise to four in the world ahead of the French Open, is only the third woman to have reached the finals at the Australian Open, Indian Wells, Miami and Rome in the same season.
The others were Monica Seles in 1991 and Maria Sharapova in 2012.
The Russian-born Rybakina has now won 28 matches this season -- only world number two and Australian Open champion Aryna Sabalenka has won more, with 29.