First-half goals from Matty Fryatt and the returning Cameron Stewart saw the Tigers roar into the play-off places in the Championship.
Both sides went into the game following back-to-back defeats prior to the international break.
After the rest, Derby welcomed back John Brayford. The right-back had been out for over a month after tearing a thigh muscle in training.
Barmby, named as caretaker manager following Nigel Pearson's return to Leicester this week, was able to call upon Stewart. The winger had been sidelined since suffering knee ligament damage in February.
Hull went ahead after 17 minutes.
Liam Rosenior embarked on a rampaging run down the right before cutting into the penalty area and teeing up Fryatt, who swivelled and shot into the top corner from 12 yards out.
Aaron Mclean drilled wide when he had a half-chance before Stewart - back after a long injury lay-off - extended the lead with his first senior goal in the 23rd minute.
Stewart's effort from the left-hand side of the area went through Frank Fielding's hands and into the roof of the net.
Derby would have been back in the game just before half-time had Peter Gulacsi not tipped Ben Davies' curler past the post.
The hosts struggled to create clear chances after the break. Tomasz Cywka had an effort blocked by Jack Hobbs just before the hour mark.
At the other end, Robert Koren saw shots blocked by Mark O'Brien and Jason Shackell.
Stewart sent a 25-yard shot narrowly wide and it was to be the former Manchester United trainee's final contribution before he was replaced by Robbie Brady after 63 minutes.
Brady made an immediate impact, forcing Fielding into a parrying save with a well-struck effort from the edge of the box.
The Irish teenager then set up Fryatt who should have really done better with his weak header in the 80th minute.
Soon afterwards, Mclean failed to get the connection he desired as he shot wide from 18 yards out.
Koren tried to add a third goal in injury time but his strike from 25 yards out went wide.