It was the highest scoring tally in a single match by a player in any national competition, surpassing the previous record of six goals held by Dinamo Zagreb striker Duje Cop.
The Croatian Cup first round result was also the biggest domestic win for a Croatian club.
The 22-year-old Kramaric was let go by champions Dinamo where he spent four difficult years in the first team after setting a club record by scoring more than 450 goals at various youth levels.
He showed his talent last season when he was loaned to city rivals Lokomotiva, netting 20 times in 45 appearances.
He scored a first-half hat-trick against Zmaj and added five in the second half as Rijeka, double cup winners in the former Yugoslavia and then Croatia, ran riot against the part-timers.
Bosnian Mehmed Alispahic scored twice and fellow midfielder Josip Brezovec added the other for Rijeka, who will meet another third division side, Podravina Ludbreg, for a spot in the last eight of the competition.