He put the Rams ahead with a left-foot shot from Morten Bisgaard's fine pass.
The same combination doubled the lead as Bisgaard's inswinging corner drew a bullet header from Lupoli's forehead.
Lee McEvilly gave Wrexham hope when he seized on Robert Malcolm's dreadful backpass, but Lupoli sealed the win when he reacted quickest to a rebound.
Wrexham boss Denis Smith:
"I thought we had a little spell at 2-1 when we possibly could have sneaked a result out of it. We had a chance which just went past a post. "If we had kept the score at 2-1 I think that would have been fair but they were excellent and we could have no complaints about the result.
"I think they are as good a team as I have seen this season and there were times when I wanted to applaud them."
Derby: Bywater, Edworthy, Moore, Michael Johnson, Camara, Bisgaard (Barnes 76), Malcolm (Smith 70), Oakley (Peschisolido 90), Jones, Lupoli, Howard.
Subs Not Used: Jackson, Seth Johnson.
Booked: Michael Johnson.
Goals: Lupoli 32, 56, 85.
Wrexham: Ingham, Valentine, Pejic, Steve Evans, Mike Williams, Crowell (Johnson 58), Danny Williams, Ferguson, Done, McEvilly, Llewellyn.
Subs Not Used: Michael Jones, Spender, Marc Williams, Gareth Evans.
Booked: Valentine.
Goals: McEvilly 61.
Att: 15,609
Ref: R Beeby (Northamptonshire).
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