The Irongate outfit have now lost five games on the bounce, coming off the back of three straight victories.
Tyrone Gay gave Ossett a 17th-minute lead.
And it was game over in the 58th minute when Jason Yates doubled their advantage.
Elsewhere in the division, Lancaster City won 1-0 at Brighouse Town, Billy Akrigg netting the only goal in the 67th minute.
Burscough had a Connor Smith double to thank for a 2-1 home win over Tadcaster Albion.
Thomas Corner put Albion into an eight-minute lead, but Smith levelled in the 28th minute.
Smith then popped up to score the winner in the last minute of the match for the Linnets.
Clitheroe went down 3-2 at home to Glossop North End after throwing away a two-goal lead given to them by Charlie Russell (4) and Kurt Willoughby (33).
North End got one back before the break when Michael Norton (42) found the net.
And late goals from Nicky Platt (85) and Jamie Rainford (87) broke Clitheroe’s hearts.
Kendal Town were 3-1 home winners against Prescot Cables.
Robert Bowman (26, 49) scored twice and Joshua Wardle (65) made the game safe before Lloyd Dean (67) scored a consolation goal.
AFC Fylde extended their league at the top of the National League North table with a convincing 5-0 victory over Stalybridge Celtic.
Star striker Danny Rowe kicked off Bonfire Night celebrations early with a dazzling hat-trick.
And goals from Dan Bradley and Steve Williams rounded off a comfortable afternoon at Mill Farm.
Rowe might have scored a fourth goal and almost had it on 70 minutes but failed to get a real connection on Bradley’s cross from close range.
The Coasters had a shout for a penalty when substitute Bohan Dixon galloped through on goal, only to be thwarted by the onrushing goalkeeper.
Rowe hit the wall with another dangerous free-kick and Richie Baker dragged a shot wide as the Coasters saw out the game comfortably to go four points clear at the top of the league.
National League outfit Southport host League One Fleetwood Town in the FA Cup first round on Monday evening.