Argyle substitute Cherno Samba went close early on, heading Darren Moore's sliced clearance goalwards and forcing Stephen Bywater to tip over.
But Derby had chances of their own with Peter Capaldi heading Moore's shot off the line and Bisgaard forcing Romain Larrieu into a smart save.
Argyle went close again through Barry Hayles before Bisgaard met Arturo Lupoli's cross to give Derby victory.
Plymouth boss Ian Holloway:
"I'm very disappointed because we looked solid at the back and I could see us breaking away to score. But we conceded because Jon Stead was very fortunate.
"We had cleared it up the other wing but Stead had been lazy and not tracked back for Derby and got it in a good position when we lost possession.
"But that was the only chance Derby had in the game and as it turned out the referee was their best defender because for some reason he pulled play back in the first half when we were on the attack with three versus three."
Derby: Bywater, Edworthy, Leacock, Moore, Camara, Bisgaard, Oakley, Jones (Barnes 46), Malcolm (Lupoli 62), Howard, Stead (Michael Johnson 89).
Subs Not Used: Peschisolido, Seth Johnson.
Goals: Bisgaard 81.
Plymouth: Larrieu, Connolly (Summerfield 90), Doumbe, Seip, Aljofree, Norris, Buzsaky (Dickson 90), Nalis, Capaldi, Ebanks-Blake (Samba 13), Hayles.
Subs Not Used: McCormick, Sawyer.
Booked: Seip, Connolly, Aljofree.
Ref: C Webster (Tyne & Wear).