The New Orleans running back picked up a whopping six rushing touchdowns in the 19-point win, equalling a 91-year-old record set by Ernie Nevers.
Kamara opened the scoring for the Saints with a brilliant 40-yard run, before Minnesota running back Dalvin Cook hit back with a 15-yard touchdown run of his own.
New Orleans responded with a one-yard touchdown run from Kamara before Will Lutz extended the lead with a field goal.
Cousins connected with Smith again shortly after to bring the Vikings back within four, however Kamara's fifth scoring run ensured New Orleans would take an 11-point lead into the final quarter.
But it was not meant to be, with Kamara's record-equalling sixth score sealing the Saints' 11th win of the season.