WATCH the WTA Tour LIVE & ONLY on beIN SPORTS | available via Foxtel, Kayo Sports, Fetch TV & beIN SPORTS CONNECT
Kasatkina, who becomes the first player to win two WTA tournaments in 2021 having claimed the Phillip Island Trophy last month, was leading 6-3 2-1 when Gasparyan pulled out.
Gasparyan initially took a medical timeout after losing her first two service games of the match to trail 4-1 before eventually retiring after dropping her serve early in the second set.
Kasatkina's triumph meant she became the first player to win both WTA 500 events on Russian soil, previously claiming the 2018 Moscow title at this level.
The former top-10 player has endured a dip in recent seasons but will be back in the top 50 on Monday, while wildcard Gasparyan's maiden WTA 500 final means she returns to the top 100.
Kasatkina dropped the opening set in her quarter-final and semi-final matches but then swept through the next two sets emphatically on each occasion.
"I'm proud of how I was able to manage the pressure," Kasatkina said, quoted on the WTA website. "I felt differently during this tournament and I'm really proud of that."