A strong Whites line-up, featuring Shane Higgs, Ben Parker, Sanchez Watt, Billy Paynter, Ross McCormack and Richard Naylor were in control from the outset at North Ferriby.
Neil Redfearn's side took the lead inside the opening 15 minutes when Paynter was brought down in the penalty area and fellow striker McCormack made no mistake from the spot.
The Tigers levelled on the half-hour mark when Daniel Emerton's shot gave Higgs no chance.
But Leeds retook the lead shortly before half-time as Paynter held the ball up and Watt showed some good footwork to score.
Paynter and Ramon Nunez also went close before Adam Clayton's excellent pass created a third goal for substitute Simon Lenighan.
United: Higgs, Thompson, Parker, Clayton, Naylor, L Turner, N Turner, Nunez, Paynter (Taylor), McCormack (Lenighan), Watt (Booker).