Shim, already with a silver medal in the 1,500-meter race, boosted the South Koreans to their fifth relay gold in the last six Olympics.
Ha-Ri Cho, Alang Kim and Seung-Hi Park joined Shim on the winning team in a race that for the second straight Olympics included a disqualification that affected the medals.
Although Shim passed Zhou Yang of China to finish first in Tuesday's race, it turned out that the South Koreans would have won the gold medal without that key maneuver.
A Chinese skater was judged to have caused an Italian competitor to fall during the event, so China's second-place finish was disallowed. Canada, which actually crossed the line third, was awarded the silver medal and Italy received the bronze.
The opposite situation occurred four years ago in Vancouver when the South Koreans finished first only to be disqualified for having impeded the Chinese. That decision ended South Korea's streak of Olympic gold medals in the event at four.
Heats were also held Tuesday in the women's 1,000-meter race and the men's 500-meter event with the United States advancing skaters in both competitions.
Emily Scott and Jessica Smith of the United States both reached the quarterfinals over 1,000-meters. Jorien ter Mors, a gold medal winner in oval skating at these Olympics, also made it to the quarterfinals.
American J.R. Celski survived his heat in the 500. Celski won two bronze medals in Vancouver, but has not had a medal finish in Sochi.