The midfielder sent in two balls within three minutes of the classic arena.
It gave Nimes a 2-0 lead against sixth-placed Olympique de Marseille and eventually a 2-1 victory.
Eliasson, with Falkenberg, AIK and IFK Norrköping as a stop on the road in Swedish elite football, left Bristol City last autumn and signed a three-year contract with Nimes in the French league.
Two goals in three minutes
After games in twelve matches, the first hits came in the 13th.
Eliasson struck in the 55th and 58th minutes, both times played by Sofiane Alakouch.
Eliasson was substituted with six minutes left.
A minute later, Marseille reduced
Nimes is fighting for its existence and remains in the relegation zone, but approached Nantes, who have two points more and are the closest lifeline in the table.