Robinson, back in the side in place of the injured Nathan Tyson, curled home the only goal of the game from inside the penalty area and Derby stubbornly defended their slender lead to follow up wins over Leeds and West Ham with another three points.
Hull mounted wave after wave of attacks in the second period, but could not find a way past Derby goalkeeper Frank Fielding as the Tigers' own play-off hopes took a further blow with a third straight league defeat.
Liam Rosenior returned at right-back for Hull in place of Paul McShane following suspension and Adriano Basso was back in goal due to Peter Gulacsi's gashed knee.
Hull dominated the opening exchanges with Slovenia international Robert Koren and striker Matty Fryatt firing in shots on target that were held by goalkeeper Fielding and blocked by defender John Brayford respectively.
Tigers defender James Chester headed Koren's 13th-minute corner inches over the crossbar and Fryatt was thwarted again, this time by visiting skipper Shaun Barker, who deflected the forward's angled drive from the right edge of the penalty area.
Hull continued to look the more dangerous side without creating further chances until the 31st minute when defender Jack Hobbs forced Fielding into a super save with his dipping goalbound volley from the edge of the area.
Fielding kept his side on level terms with an even better save eight minutes later, diving low to keep out Fryatt's angled effort from 12 yards following Paul McKenna's cross, but for all Hull's possession the score remained goalless at the interval.
Derby then stunned their hosts with a goal just 32 seconds after the restart.
James Bailey crossed from the left and, after dancing clear on the left-hand side of the penalty area, Robinson curled a left-footed shot beyond Basso for his seventh goal of the season.
Buoyed by their unexpected breakthrough, the Rams enjoyed their best spell of the game.
Striker Jamie Ward's drilled free-kick was well held by Basso and midfielder Paul Green curled a right-footed shot from the right edge of the area just wide.
Hull responded with their first chance in the second half, defender Andy Dawson heading Cameron Stewart's cross over the crossbar in the 58th minute, while Koren lashed in another long-range shot that Fielding comfortably held soon after.
Tigers manager Nick Barmby sent on Manchester United loanee Robbie Brady with half an hour to play, while Rams boss Nigel Clough swapped teenage striker Callum Ball with midfielder Ben Davies.
Hull threw everything at Derby as the game entered the final 20 minutes. Brady's angled drive was blocked by Derby central defender Jason Shackell and Fryatt headed weakly at Fielding following McKenna's cross.
Koren attempted a trademark effort from outside the area, but again Fielding was equal to it and the visitors held firm throughout five minutes of added time.
