They had the better of the opening play, but Ossett shocked them by taking the lead after 17 minutes when Chris Wood headed in from a corner.
Gavin Cogdon was just off target for Moors before they equalised on 39 minutes when Chris Mason’s effort from a corner was blocked, and Gavin Cogdon set up Joe Tait to score from the loose ball.
Moors went into the lead from a breakaway just before half time, when John McReady played a 1-2 with Liam Henderson and tucked the ball in.
Sub Michael Roberts had a third goal disallowed midway through the second half, then Henderson was just off target.
Moors made the game safe two minutes from the end when the keeper spilled a Roberts cross and Stephen Capper scored from the rebound.
Ossett had defender Sam Holt red carded for a two footed tackle on Henderson in stoppage time.
Moors boss Jason Ainsley said; “We didn’t start very well, maybe because it was a knock on from the Prescot game, and we went a goal down.
“But once we equalised, we were more our usual selves. The two goals before half time put us in the driving seat, and the confidence was oozing after the third goal.
“It was a good three points, because teams will become a cropper there. With the Padiham away game, that’s two awkward away games out of the way.”