Derby remain in the hunt for automatic promotion from the Championship after their 1-0 win over Luton Town confirmed the Hatters' relegation to League One.
Nyatanga scored his second goal of the season
Matt Oakley hit the bar and Steven Howard had a header cleared off the line before the Rams took the lead with Lewin Nyatanga's close-range finish.
Giles Barnes headed against the bar for Derby after the break and Talbot missed a good chance to grab an equaliser.
Rams keeper Stephen Bywater then denied Besian Idrizaj with a fingertip save.
Derby manager Billy Davies:
"It puts a bit of pressure on one or two teams.
"It was a 'must-win' game. Unfortunately we only scored one goal and that made us nervous.
"We are in the early stages of development. I've been here 10 months, but I'm delighted by our progress."
Luton manager Kevin Blackwell:
"The players put on a a terrific performance. I'm so proud of them and this has definitely given me something to work with.
"We dominated large parts of the game, but we lacked a that bit of knowledge.
"We've a dynamic new chairman and with some of the young players we have the club has a future."
Derby: Bywater, Edworthy, Leacock, Nyatanga, McEveley, Teale (Pearson 73), Oakley, Jones, Currie (Lupoli 65), Howard, Barnes (Fagan 80).
Subs Not Used: Grant, Mears.
Goals: Nyatanga 37.
Luton: Brill, Foley, Coyne, Barnett, Emanuel, O'Leary (Langley 73), Spring, Heikkinen, Bell, Andrew, Talbot (Idrizaj 65).
Subs Not Used: Perrett, Boyd, Keane.
Ref: R Beeby (Northamptonshire).