Hinckley Leicester Road kept themselves within touching distance of the play-off zone with an ultimately comfortable win at Butlin Road.
Despite the final scoreline, Rugby had made a decent fist of things in the first half in particular, and they were still very much in the game until the visitors opened up a two-goal differential just before the interval.
However a much less eventful second period followed, and Rugby's threat diminished as Hinckley added to their total and saw out the game effectively.
There was a Valley debut for new signing Demico Burton at left-back, with Roger Lee also back into the starting line-up in midfield.
Hinckley established an early lead on seven minutes when Aaron Nuttall skipped past several Rugby defenders before applying a low finish past Nykah Liburd-Hines.
Town were level within a hundred seconds though, when Ryan Sahota eased home Silvano Obeng's ball across the goalmouth after good interchange play on the right between David Kolodynski and Chris Clements.
The visitors looked to re-establish their lead, with Tendai Daire's shot on the turn blocked well by Liam Francis.
Hinckley's second of the afternoon did soon follow though, when more Nuttall trickery set up Daire for a shot that squirmed out of the grasp of Liburd-Hines at his near post.
The dangerous Nuttall then shot wide of the target after Louie Gill had played him in, and Andre Williams's effort from a central position in the box was straight at the Town keeper, as the Leicestershire side looked to further turn the screw on the hosts.
Rugby managed to up their game too though, and put in an impressive spell for the remainder of the half.
A Chris Clements ball in behind the Hinckley back-line found Kolodynski in space, but the striker's resulting low strike was pushed away by Will Highland, with Obeng's cross of the loose ball blocked away.
Obeng's header to a Kolodynski looped cross was also saved by Highland, before Jordan Wilson whipped one wide following a purposeful run from the impressing Burton.
At the other end, Jordan Burrows did have a goalbound effort blocked by his own team-mate Liam Read, but Town's pressure continued with another surge forward by Burton ending with a dangerous cross that was cleared away for a corner.
However, Town were struck with a hammerblow on the stroke of half-time when Sahota fouled Nuttall just inside the penalty area, and although Liburd-Hines managed to keep out Daire's resulting spot-kick, the Hinckley marksman followed up on the rebound to power the ball into the net.
Rugby were barely able to lay a glove on their opponents after the restart, as the Knitters underlined their promotion potential with a measured, controlling performance.
Liburd-Hines denied Nuttall with a decent double stop, before Hinckley extended their advantage further after the Rugby keeper was bizarrely penalised for not taking his kick-out quickly enough, with Daire completing his hat-trick goal by heading Callum Earls's delivery in off the post from the awarded indirect free-kick.
The two final chances of a gradually petering out affair both fell to Rugby, with Lee's half volley always rising above the target and then Drew Kear had a shot blocked from a dangerous position, after the Town sub had dispossessed Earls before running into the box.
