The visitors were forced into two late changes as George Breese and Luke Graham were both taken ill overnight, James Baker taking over at tight-head and Tomek Pozinak on the wing – Ryan Lomas stepping up to the bench – but they started brightly,
Two early opportunities came and went, Zach Clow firstly bursting through before Morgan MacRae was just unable to gather a Ben Atkins off-load with the line at his mercy.
Atkins then reached for the whitewash only to be penalised for a double movement, but Leeds were penned inside their own half for the opening 30 minutes.
And they eventually lost No. 8 Eddie Brown to the sin-bin following a cynical breakdown infringement, Axel Kalling-Smith having got his side on the front foot with a trademark powerful burst.
MacRae puts visitors in front
Rams took the lead shortly after, relentless pressure eventually converted as MacRae crossed for a score added to be Mike Cooke.
The try seemed to ignite the hosts, however, and they posted notice of their intent as Ed Crossland beat several defenders before the ball was eventually knocked on 10 metres short of the try-line.
But it was Tykes who started the second period stronger, levelling matters as Ben Dixon dotted down following a series of close-range carries before Crossland slotted the extras.
Rams then began to shoot themselves in the foot with numerous silly penalties in midfield allowing their rivals field position during the third quarter.
Yet the away scrum had been powerful throughout, centurion Ant Marris and Baker dominant before Paddy Harris and Lomas continued the good work, and several set-piece penalties kept them in the contest.
Discipline costs Tykes late on
Leeds were again reduced to 14 men as Tom Collins was carded for taking a player in the air at a line-out, and Aarin Yorke swiftly followed for a deliberate knock-on on his five-metre line.
Tykes were incredibly then down to 12 as Will Dennis followed, but having butchered a chance with a forward pass, Rams eventually put the ball through the hands for Clow to dot down on the right.
Captain Max Hayman then peeled off a maul to extend the lead, Cooke with a lovely touchline conversion, and suddenly dreams of a bonus-point were lifted.
Those hopes heightened when Will Yates became the fifth Leeds player to be carded, a dangerous knee on Clow the cause, but try as they might, the visitors could not score the fourth try.
Rams host Birmingham Moseley next Saturday (3pm). For tickets, click here
