Going into the encounter goalless after the first leg, the hosts flew out of the traps to all but put the tie beyond doubt with a 3-0 lead at the interval.
Brian Stock opened the scoring from the penalty spot after eight minutes while Southend skipper Adam Barrett put through his own net shortly after to put the home side firmly in control.
Coppinger contributed with a superb individual goal prior to the break, before adding an almost identical second at the other end seven minutes after the restart.
The midfielder then completed his treble with a sublime free-kick in the 79th minute. Nicky Bailey registered a late consolation for Southend.
The result leaves Doncaster, who missed out on automatic promotion on the last day of the season, just one game away from a return to second-tier football for the first time since 1958.
It also means victory against Leeds on May 25 would seal a remarkable journey from non-league football to the Championship in the space of five years.
The result at Keepmoat Stadium crushed Southend’s hopes of an immediate return to the Championship.
DONCASTER: Sullivan, O’Connor, Mills, Hird, Gareth Roberts (Guy 68), Green, Stock, Wellens (McCammon 73), Coppinger, Price (Taylor 76), Hayter.
SOUTHEND: Flahavan, Francis, Clarke, Barrett, Mulgrew, Moussa, Bailey, McCormack, Gower, Barnard (Revell 62), Walker (MacDonald 62).
Referee: Mark Halsey (Lancashire).