A Paul Rich penalty was the only score for Southwell as they suffered a home loss to Matlock.
The result leaves them in a relegation scrap, as they look to secure their Midlands Division Two East (North) status.
With three matches left, they are third from bottom on 29 points, two ahead of Nottingham Casuals and four in front of Loughborough.
Matlock, in contrast, are chasing a play-off spot and were simply too strong for Southwell as they achieved a comfortable victory.
Rich scored a penalty in the first-half, but Southwell were unable to penetrate a strong Matlock defence in bitterly cold conditions.
Despite the dominance in the scrum and line-out, they couldn’t make their chances count.
The match was still in the balance until late in the second-half, but Southwell were undone by three late tries, which gave the scoreline a flattering look.
Southwell are back in action on Saturday when they host runaway leaders West Bridgford.
Newark 1sts, who didn’t have a match at the weekend, are next in action on April 14 at Coalville.
Market Rasen 2nds 31 Newark 2nds 15
A young Newark side put up a spirited display as they fell to defeat in their match against Market Rasen.
They were in touch with their opponents for much of the match, until their opponents pulled away with some late scores.
Hindered by a first-half injury up front and a sin-binning, Newark turned round 12-8 down.
They put pressure on early in the second-half to cut that margin.
Newark’s first try came from winger James Harding, who latched on to a pass from full-back Josh Clack in the first-half following two tries from Rasen.
Harding scored a second nimbly late on but by then Market Rasen had the match won.
Newark fielded a mostly young team backed by a few first teamers and former captain Nick Codd.
There was a 36-5 loss for Newark 3rds against Kesteven.