Elina Babkina, who finished with a game-high 21 points, got Latvia to within three (44-41) on a hard drive to the glass in the opening seconds of the third period.
Russia then looked to Grishaeva, getting her the ball on the low post. She did not disappoint, scoring on four straight possessions to take her team to a 52-43 lead.
Latvia was able to stay close through the game by pushing the ball off Russia's 20 turnovers.
Russia led early 9-2, but Latvia came back and jumped ahead 10-9 on a lay-up by Babkina.
Russia's Elena Pavlova (13 points) then nailed back-to-back three-pointers to reclaim the lead for good (15-10) and her team would end a high-scoring first quarter 29-21.
Grishaeva put Russia ahead by ten (36-26) after a possession in which she grabbed three offensive boards in a row before putting it in.
Latvia got to within five points, but another timely Pavlova triple pushed Russia out to a seven point lead.
Two free throws by Babkina with :00.3 on the clock cut the difference to only five at the half (44-39) before Grishaeva took care of business in the third period.
"We feel really confident," said Grishaeva about Russia's prospects for the tournament.
"We will do our best even though it will be tough because we have our main players who have been playing thirty minutes each game, but we are ready and we are going to go out there and fight."
Russia play Lithuania thinking about their position in the Quarter-Finals' match-ups.
Latvia were without Baiba Eglite who did not play do to a knee injury. She is almost certain to miss tomorrow's game against 4-0 France as well.