The result means Nigel Clough's side finish the campaign in 12th position on 64 points - the Rams' third-best tally in the last 16 seasons.
Peterborough United arrived at Pride Park safe in the knowledge that they were playing Championship football next season, and the Posh showed their attacking intent in the opening two minutes as Lee Tomlin ran at the Derby backline and unleashed a low shot that drifted wide of Adam Legzdins' far post.
However, the Rams responded with chances of their own and on eight minutes, Will Hughes and John Brayford combined brilliantly down the right, before the latter delivered a low cross to Steven Davies, who volleyed goal-wards and forced Paul Jones into an excellent reflex save.
Two minutes later, former Tranmere forward Davies stung the fingertips of Jones with a ferocious free-kick that found a way through the Peterborough wall.
The Rams' dominance was soon rewarded through Robinson. Craig Bryson curled in a cross-come-shot from the left and Robinson got the final touch to send the ball past Jones from inside the six-yard box.
Robinson's goal moved the former Millwall striker on to 12 for the campaign, level with strike-partner Steven Davies.
Clough's men continued to control proceedings and had numerous opportunities to double their lead ahead of the half-time whistle.
Player of the Season Bryson saw a long-range effort palmed behind, whilst defender Jason Shackell glanced Hughes' resulting corner inches wide of goal.
Another three chances followed in the space of nine minutes; the impressive Hughes saw a close-range volley blocked on its way to goal, before the Academy youngster turned provider and sent Bryson clear down the right. The former Kilmarnock midfielder half-volleyed across goal, but unfortunately for the Rams, the ball somehow managed to evade the onrushing Davies.
Five minutes before the interval, Bryson's clever through ball found Robinson, who spotted Jones off his line, but the 23-year-old's speculative effort was claimed at the second attempt by the former Exeter City 'keeper.
Bryson almost got the Rams off to a flying start in the second-half with a long-range effort that flew narrowly wide.
The visitors reminded the Rams that they were only a goal behind moments later, as Tommy Rowe's bursting run won a free-kick on the edge of the home side's penalty area. Grant McCann's initial effort was blocked by the Derby wall, but the ball fell kindly to Craig Alcock, who rifled the rebound at goal, but Jake Buxton was in the way to avert the danger.
The Rams thought they had secured an elusive second goal when Davies turned in Robinson's low cross from close-range, but the 23-year-old was adjudged to have been offside.
In the 74th minute 15-year-old striker Mason Bennett replaced goal-scorer Robinson, who left the field to a rapturous applause from the Derby County supporters.
And it was Bennett who almost made an immediate impact. The Academy youngster released Tyson down the left who found Hendrick in the penalty area. The Irish under-21 international fired low at goal but his effort was well blocked by a combination of Alcock and Jones.
However, the Rams were left ruing their missed chances as against the run of play, Ferguson's men equalised with eight minutes remaining.
Former Manchester City striker David Ball beat the offside trap and coolly curled the ball past Legzdins into the top corner, to stun the Rams.
It could have been even worse for Derby as in the final few minutes George Boyd created room for himself in the penalty area and fired an effort that shaved Legzdins' near post.
Derby County: Legzdins (GK); Brayford, Buxton, Shackell, Roberts; Hughes (Carroll 83), Hendrick, Bryson (Bailey 87), Tyson; Robinson (Bennett 74), S. Davies.
Subs Not Used: Thomas, Lelan.
Peterborough United: Jones (GK); Alcock, Zakuani, Little, Rowe; Tomlin, McCann, Newell (Ntlhe 56); Boyd, Barnett (Ball 63), Taylor (Kearns 56).
Subs Not Used: Brisley, Grant.
Attendance:27,354 (1,741 Peterborough United Supporters).