The visitors were up against it from the start and, after Dillon Morse had headed Shields in front, their task was made even harder when striker Nicky Boshell was sent off for a foul on Julio Arca.
The Mariners pushed on from there, with Robert Briggs making it 2-0 from the penalty spot before Gavin Cogdon, Julio Arca and Louis Storey all netted in the second half to complete the job.
Hyde United’s draw at Bamber Bridge allowed Shields to climb back to the top of the league and strengthen their promotion bid.
They were on the front foot from the start against Ossett, and almost took the lead early on when Carl Finnigan’s effort was cleared off the line.
Jon Shaw headed wide from a Robert Briggs free-kick as Shields continued to probe, and their breakthrough arrived in the 14th minute as Arca’s cross from the right was headed in at the back post by Morse.
Boshell was sent off in the 21st minute for an awful challenge on Arca in the centre of the park, and there was no way back from there for Ossett.
It was soon 2-0 when, after Cogdon was fouled in the area, Briggs stepped up to rattle the penalty away and surely make the points safe.
Jamie Holmes and Storey went close before half-time, but a five-minute blitz in the second half ultimately added the gloss to the scoreline.
Cogdon scored Shields’ third as he tapped into an empty net following a fine move, with Darren Lough stroking the ball across the box for him.
Arca was soon in on the act, too, as he reacted quickest when a Briggs drive was parried to find the net.
And then it was Storey who completed the scoring as he diverted another Briggs shot from distance in via his head.
The Mariners could have made the scoreline even more convincing in the closing stages, but ultimately kept the ball and conserved some energy ahead of a hectic period.
Shields travel to Workington in the quarter-finals of the League Cup tomorrow.
SOUTH SHIELDS: Connell, Baxter, Lough, Shaw (Smith 63), Morse (Mason 71), Arca (c), Storey, Briggs, Cogdon, Finnigan (Richardson 34), Holmes. Subs not used: Woolston, Goals: Morse (14), Briggs (pen 25), Cogdon (62), Arca (65), Storey (67).
In the TWR Bifolds Wearside League, fourth-placed Boldon CA held second-top Hebburn Town Reserves to a 1-1 draw.
The visitors were ahead from a corner in the third minute, but Hebburn rallied. Josh Houghton went close on 26 minutes, when his shot grazed the bar, and they equalised after 64 minutes, Daniel Maddison smashing home a fierce shot.