The local derby honours were even, after David Kolodynski's 70th-minute strike saw the hosts come from behind to secure a point.
Town deservedly emerged with some reward from a tight, cagey affair at Butlin Road and this first home draw of the league campaign duly lifted them off the bottom of the table ahead of the final two games of the season.
Rugby were unchanged from their victory over Shepshed the previous week, but it was the visitors that had the first chance of the game when Elliot Parrott's header to a corner to the back-post was comfortably gathered by Tomasz Bukowski.
Madundo Semahimbo had already blazed one over the bar when he forced a neat one-handed save from Bukowski's counterpart Liam O'Brien after his initial shot had been blocked, with Bukowski then back in the action at the other end by parrying away a low strike from Liam Murphy.
The hosts then enjoyed their best spell of the entire match in the mid-part of the first half, with a string of opportunities for them kicked off by Kolodynski just being unable to get on the end of Michael Taylor's header to a neatly-delivered free-kick by Chris Clements.
Kolodynski poked one into the side netting after good work by Semahimbo, before Theo Rowe and Semahimbo had shots blocked in the same passage of play and Rowe had a further effort from the edge of the penalty area acrobatically pushed away by O'Brien.
Bedworth rallied a little ahead of the interval, with Bukowski safely dealing with ex-Valley youth teamer Leo Stone's low shot and another one-time Butlin Roader Stephan Morley's attempt from long distance. Murphy also blazed over just before a half-time whistle which signalled a goal-less opening period, with Town missing the first chance of the new one when Liam Francis's close-range header to Loyiso Recci's hooked delivery lacked power and was caught by O'Brien.
The Greenbacks broke the deadlock on 50 minutes though when Morley's pass in behind the Town back-line was taken on by Murphy and he slotted past Bukowski.
Rugby responded well to the setback, with Taylor's effort from twenty yards blocked and then Francis just failing to force home Recci's header back across the face of the goal. Murphy almost added his second when he dispossessed Recci in a dangerous position, but Bukowski was out quickly to narrow the angle and deny the United striker.
Bukowski also turned a goalbound Murphy header around the post, before Town levelled things up in somewhat fortuitous circumstances when O'Brien spilled a Clements corner onto his right-back Ryan Moore for it to fall nicely at the feet of Kolodynski to ram the ball home from a yard out.
The visitors arguably had the best of the remaining twenty minutes or so, with Bukowski saving well from Stone, and Recci clearing away a dangerous cross from Moore.
Parrott and Murphy both put in off-target headers, and shortly after that Francis just managed to hook away the ball from Murphy with the striker poised to shoot.
The final chance of the game fell to Valley in the final few seconds though, with Francis unable to force home another Clements set-piece delivery - although the Rugby defender was ultimately adjudged to have been in an offside position anyway.
