Long Eaton won the battle of the out-of-form sides at Butlin Road as Valley fell to another defeat.
Once again it was a story of Town falling the wrong side of the line of a game decided by fine margins as they registered their tenth single-goal loss of the league campaign so far against opposition that had been on a poor run of results of their own beforehand.
The decisive blow was ultimately struck for United by ex-Valley striker Jahvan Davidson-Miller on 53 minutes, after Town debutant Tyler Bruck had scored on his debut just before half-time to even up the scoring.
Bruck was joined in Rugby's starting line-up by fellow new arrival Bo Morris in two of six changes made from the previous week's 3-0 home defeat to Rushden with Archie Murray, Josh Thomas, Teddy Rowe and Xander Grieves also back - in addition to a formation switch to three central defenders.
With both sides having not won for seven games, confidence was low in both camps and quality was at a premium from the off, and it was Grieves that became the first keeper called into any real action when he pushed away a dangerous cross from the left by Davidson-Miller.
Jayden Cockerill headed one over as the visitors continued to probe for a breakthrough, but their opening goal did come on 21 minutes when Thompson-Matthews executed an impressive acrobatic volleyed finish at the back post to a nicely-flighted cross from Owen Betts.
Davidson-Miller then had an on-target strike blocked in the box by Thomas, with Evan Garnett also sliding a decent chance wide of the post from a tight angle as United looked to double their advantage.
Rugby finally had their first sight of goal when Ryley Nicholson just failed to get a proper connection to Teddy Rowe's corner before the ball bounced agonisingly away to safety.
Town got themselves level just before the interval though, when Bruck timed his run to perfection to beat the Long Eaton offside-trap and run onto Morris' ball over the top and neatly clip the ball over Lewis King into the net.
The hosts started the new period brightly, and King's handling was secure to Murray's cross from the left after Jack Concannon had played him in.
However, United were back in front again after neat interchange play between James Taylor, Garnett and Thompson-Matthews created the opening for Davidson-Miller to help the ball into an empty net after Grieves had managed to block his initial one-on-one effort.
Garnett drilled one just wide from the edge of the box, before Rugby nearly grabbed another equaliser when sub Rivel Mardenborough was smothered out at close quarters after Bruck had sent in a low cross from the right, and then Murray's effort to the resulting loose ball was fumbled by King into the path of Mardenborough to help it home - only to see a flag up for offside.
An excellent through ball from Caine Elliott then released Bruck down the middle again, but this time King was able to thwart him just inside the penalty area and then grab the ball at the second attempt.
Thomas headed one over at the near post, with Concannon also firing marginally high of the frame with his shot on the turn, as Valley continued to push purposefully forward.
At the other end, George Atwal's strike from distance was comfortably gathered by Grieves, whilst Mardenborough skied one against the top of the stand after Jamal Adams had done well to steal possession and slip him in ahead of the sound of another disappointing final-whistle for Town.
