Michael Bostwick gave Posh the half-time lead before a late double from on-loan striker Saido Berahino moved Darren Ferguson's side out of the bottom three ahead of the evening kick-off between Bristol City and Hull.
Posh went ahead after half an hour when Bostwick fired into the top right-hand corner of the goal and had a couple of chances to immediately double their lead.
George Boyd, brilliant against Huddersfield, forced a good save from Legzdins with a 20-yard effort.
Adam Legzdins then tipped over a shot from Berahino when the West Brom teenager threatened from the left side this time.
Conor Sammon failed to get Derby back on level terms after 40 minutes, firing wide from just six yards out.
Robinson came even closer to an equaliser five minutes after half-time when his shot from 12 yards out struck a post.
Tomlin should have put Peterborough 2-0 in front in the 57th minute after Richard Keogh brought down Boyd inside the area but Legzdins saved the resulting penalty.
Derby's task got more difficult when Jake Buxton was booked for the second time in just four minutes. The centre-half's fouls on Berahino and then Boyd resulted in him being sent off after 70 minutes.
And from the following free-kick, Legzdins produced more heroics to keep out Bostwick's shot.
Legzdins then thwarted substitute Danny Swanson with another parrying save but he undid some of his good work with four minutes remaining when he dropped Berahino's shot from the edge of the area over his own goalline.
Berahino added some gloss to the scoreline deep into injury time when he breached the Derby defence and raced clear to beat Legzdins once more.