Sven-Goran Eriksson took a squad containing eight summer signings to the Don Valley Stadium but it was debutant Schlupp, who had a successful loan spell at Brentford last season, who shone.
An own goal from Matt Mills gave the League Two club an early lead. Paul Gallagher brought Leicester level before the break and Schlupp took over after it.
Mills, along with fellow defender Paul Konchesky and goalkeeper Kasper Schmeichel, was just one of three survivors from the team that started the Championship victory at Coventry on Saturday.
And the club record signing gifted Rotherham the lead after 13 minutes when he turned Adam Le Fondre's cross past Schmeichel.
Schmeichel saved a Ryan Cresswell header to keep Leicester in it just after the half hour.
It was against the run of play when Gallagher headed Eriksson's side level from Martyn Waghorn's cross in the 36th minute.
Schlupp put Leicester in front with a shot across Andy Warrington eight minutes after the restart, and he beat the Rotherham goalkeeper again just after the hour with a header from Gallagher's cross.
The Ghana-born Germany Under-19 international completed his hat-trick in the 71st minute from close range after Warrington could only parry Gallagher's shot.
Warrington denied Leicester a fifth goal when he saved from Waghorn late on.