Billingham’s robust defence frustrated Slazenger early on but the Horbury men recovered to win comfortably in the end. Nick Webb fired in a fierce shot to open the scoring, but Billingham replied with a breakaway goal and things looked worrying for a while.
But Kevin Windler settled Slazenger nerves with a solo run from halfway and an excellent finish from a tight angle.
And Keith Whittle sealed matters when he followed up well from a short corner.
The valuable three points ensure Slazenger retain fourth place in the North East Division 2 table.