Nyatanga played the full 90 minutes at the heart of the Rams defence and Teale came on with half an hour left.
Kris Common's blistering strike in the 30th gave Derby the win and takes them to Old Trafford with a goal cushion in the second leg.
Spurs beat Burnley 4-1 in Tuesday's other tie with goals from Michael Dawson, Jamie O'Hara, Roman Pavlyuchenko and an own goal by Michael Duff wiping out Martin Paterson's early goal for Burnley.