The Tigers roared into the automatic promotion spots with a confident display at Oakwell which halted Barnsley’s recent renaissance.
Marney held his nerve to convert a crucial first-half penalty after Dennis Souza felled Fraizer Campbell and then set up Ian Ashbee for his side’s second.
Sub Dean Windass added a third with his first touch to take his tally for the season to 13 and wrap up three precious points for Phil Brown’s men.
Campbell produced yet another eye-catching display for Hull, who have lost just one of their last nine games. The 20-year-old striker, on-loan from Manchester United, terrorised the Tykes, who remain perched above the drop zone and pulled a goal back late on through Istvan Ferenczi.