Theo Robinson's 22nd-minute goal has given Derby County a 1-0 lead at half time.
The away side made a bright start and created the first chance when Lee Tomlin showed good composure to burst through midfield, but he dragged his 25-yard shot just past the post.
Derby had a chance on nine minutes, but goalkeeper Paul Jones produced a stunning save to deny Steve Davies, diving to his left to claw the ball away from danger.
Moments later, Jones was called into action again, denying Davies's low free kick from 30 yards with another fine save.
A good run to the by-line by Paul Taylor produced an opportunity for Tyrone Barnett, but he stabbed his volley straight at goalkeeper Derby shot-stopper Adam Legzdins.
On 22 minutes, Derby went 1-0 up after a cross from the left by Tyson was guided home at the near post by Theo Robinson.
The Rams had appeals for a spot kick turned down on 27 minutes as Boyd appeared to tug down Tyson, but the referee waved away the players' protests.
On 42 minutes, Tomlin's powerful 30-yard drive whistled just past the upright as Posh came close to a leveller before half time.
However, the score stayed the same as the referee blew the whistle, with Derby 1-0 up.
