Town were left ruing a number of missed chances after they made the short trip home from the Oval with just a single point.
The visitors were the better side in Easter Monday's local derby and had taken the lead thanks to Chris Sterling's 50th minute strike, but United levelled just after the hour mark to send Valley into the final game of the season with their fate no longer in their own hands.
Aiden Print and Robbie Parsons both returned to Rugby's starting eleven in place of Gary Moran and Aaron Moses-Garvey, and Town made a decent start to the match with Levi Rowley firing a shot off-target from twenty yards after good build-up play.
Sterling then struck the inside of the upright after he had dispossessed Mark Allbrighton and skipped through a couple of challenges, with Ryan Quinn firing over from the edge of the penalty area and Rowley also having a further effort on the turn saved by Josh Barnes.
Barnes executed another comfortable stop to Sterling's curler ahead of the interval, but he could not stop the same player's low strike five minutes after the restart.
Bedworth sub Iyseden Christie had a header cleared off the line by Print as the hosts looked to get back on level terms, with David Kolodynski then missing a gilt edged opportunity to increase Valley's lead when he rushed his effort after Mitchell Thomson had played him clean through.
That miss proved crucial as Jack Jeys equalised when he ran through onto ex-Town midfielder Richard Blythe's incisive pass to lift the ball over the head of the advancing Louis Connor on 63 minutes.
Rugby went on to create a number of chances for a winner in the final half an hour of the game though, with Barnes keeping out Levi Rowley's powerful shot, Kolodynski again failing to capitalise on another opportunity in behind the Bedworth defence and Quinn's shot from just inside the area also saved by the busy Greenbacks' stopper.
At the other end, Luke Rowe's free-kick drifted just wide and Connor made a good save to keep out a Christie header, with Valley's final effort of the game seeing Levi Rowley put one just the wrong side of the frame after Sterling and Quinn had combined well to create the opening.
Line-up: Connor; Print, Brathwaite (Punter), M Rowley, K Rowley; Quinn, Thomson; Parsons (Shakespeare), Sterling, L Rowley; Kolodynski. Subs not used: Fura, Moses-Garvey, Faulkner. Booked: Quinn, Punter.
Bedworth line-up: Barnes, Kavanagh, Rowe, Walters, McAteer, Albrighton, Parrott, Blythe, Ciolek, Jeys, Perkins. Subs: Amour, Christie, Cross, Brehon, Haines.