That total made her the winner by less than a tenth of a point over Polina Astakhova, who like Latynina was a Ukranian representing the Soviet Union at the Tokyo Games.
It was the 18th and last medal won by Latynina during her Olympic career and so far, no one has ever won more.
Latynina's mark for most medals won is at the top of the list of Olympic records, but after nearly a half-century, it will almost certainly fall at the London Games.
Michael Phelps, already holder of the record for most gold medals in both a career and a single Olympics, arrives in London with 16 overall medals. He is scheduled to swim in seven events and is expected to at least medal in all of them.
If he does so, the 23 total medals he will have won will probably stand as the pinnacle for Olympic achievement much longer than has the mark established by Latynina.
The sports of gymnastics and swimming are the only ones on the current Olympic program in which an athlete can realistically pile up the hardware. There have been 33 competitors who have won at least six medals in one Olympics and 27 of them have been either a swimmer or a gymnast.
Phelps won eight medals at the Athens Olympics in 2004 (six of them gold) and added eight more in Beijing four years ago. All of the medals Phelps won in China were gold, breaking the single-Olympic record of seven established by Mark Spitz in 1972.
This time Phelps made reduced his workload slightly. He will swim in both the 200- and 400-meter individual medley, the 100- and 200-meter butterfly and three relays.
One of the most anticipated events of the entire Games, in fact, will come on the first full day of Olympic competition.
At 7:30 p.m. local time (2:30 p.m. EDT) Saturday, July 28, the finals of the men's 400-meter individual medley will take place.
Phelps and American teammate Ryan Lochte will likely battle for the gold medal and a victory by Lochte would not be a surprise. Lochte defeated Phelps in the event at the U.S. Olympic trials.
Phelps is not the only American swimmer who could collect a haul of medals in London.
Lochte, who won six medals in Beijing, could easily run his career total to at least 10 during the upcoming games. That, however, would obviously still leave him far short of Phelps' career total.
Missy Franklin is in position to swim in seven finals, something no other American woman has ever done at the Olympics. Franklin, 17, won three golds at the most recent world championships and she could leave London as one of the superstars of the Games.
But even if she should win seven medals, Franklin would probably have to compete in three more Olympics to have a chance to challenge for the all-time record that Phelps is likely to set.
When Latynina completed her Olympic career with 18 medals, it seemed to be a record that might never be broken. On the assumption it is broken, the same thing will likely be said about the new one.