Felix, who on Friday became the most decorated female track and field athlete of all time with a bronze in the individual 400m, helped a 'Dream Team' US quartet romp home in 3min 16.85sec.
Poland took silver, while Jamaica took bronze.
The USA fielded a star-studded line-up which included world record-breaking 400m hurdler and newly crowned Olympic champion Sydney McLaughlin, 400 hurdles silver medallist Dalilah Muhammad and teenage 800m gold medallist Athing Mu alongside the veteran Felix.
With McLaughlin getting the American women off to a blistering start before handing off to Felix on the second leg, it soon became clear that the US quartet were racing against history and the Soviet Union's 33-year-old world record of 3:15.17 set at the drug-tainted Seoul Olympics.
But while Muhammad built up a massive lead for Mu with a blistering third leg, the record remained just out of reach with the 19-year-old from New Jersey crossing the line four seconds clear of Polish anchor runner Justyna Swiety-Ersetic.
Felix, 35, is competing in her fifth and final Summer Games and now has 11 total Olympic medals, extending her record as the most decorated female track and field Olympian in history.
Her 11th medal also took Felix one clear of Carl Lewis' 10 medals as the most decorated US track and field Olympic athlete.