Valley lost out in the local derby against Coventry Sphinx to make it three league defeats in a row as both sides ended with ten men.
Luke English had given Rugby a first-half lead, but the visitors levelled things up from the spot just past the hour mark before Sphinx's Matty Shipman struck a winner past Town's scorer English - who had taken over the gloves following the sending-off of debuting Valley keeper Nykah Liburd-Hines in the aftermath of the successfully converted penalty.
Town's starting line-up had five changes from the previous outing, with fellow new signing James Mace joining Liburd-Hines in making a first appearance for the club, and Loyiso Recci, Liam Francis and Jordan Wilson all back in.
Shipman had two early good chances to open the scoring for Coventry, when he first dragged one wide from a decent position and then he was denied by an excellent diving header on the line by Ryan Sahota.
Sahota was soon causing problems of his own at the other end of the pitch though, with Sphinx keeper Keelan Fallows smartly off his line to prevent him from getting onto a neatly delivered searching pass by Wilson, and then Sahota nearly managed to hook home a Barry Fitzharris corner that had been helped on by the head of Liam Francis.
Rugby's increasingly promising play then saw Wilson's shot from a tight angle gathered by Fallows, although Liburd-Hines did turn round a low effort from Callum Woodward around his post, and Parker's bundling strike was also deflected wide.
An English long-throw was met by Francis's head again - forcing Fallows into a good save, with Valley's goal then coming in the 32nd minute when English hooked the ball just over the line after Wilson had prodded it forward from Fitzharris's original corner.
Town pushed for an immediate second, with Sahota's header to another English hurled delivery into the box parried away by Fallows.
A further surge into the box by Sahota ended with a strike over the bar, and Wilson also put one high of the target with his head shortly after.
Liburd-Hines was called upon for a reflex stop to Shipman's header ahead of the interval, with Finlay Shorrock also missing out with a free-kick from a potentially dangerous position before the two teams retired.
Wilson headed a Fitzharris corner over in the opening minutes of the new period, before Edwin Ahenkorah missed a great chance to put clear space between the sides when could not keep his shot down from ten yards out after Wilson had shown good strength to see off William Edjenguele before picking out Ahenkorah with his cross.
Parker tested Liburd-Hines with a rising volley from the edge of the box, before the game turned when Recci was adjudged to have clipped Jac Redhead just inside the area to allow Woodward to step up and stroke the ball home from the spot.
Liburd-Hines was then red-carded after Woodward went down theatrically as the Sphinx skipper retrieved the ball from the net, with subsequent video evidence showing the absence of violent conduct in any contact made between the players - meaning English took over between the sticks for the remaining half an hour so.
The numbers were immediately evened up though, when straight from the restart Jack Downes received his marching orders after his late tackle on Sahota earned him his second yellow of the afternoon.
English was relatively untested and untroubled by the visitors until Shipman fired one into the bottom corner from Parker's lay-back, with Redhead going close to adding to the tally when his strike from the angle flew wide.
Rugby offered a limited threat only after falling behind, although their third debutant of the day young striker Harvey Kirby-Moore nearly got on the end of a Wilson flick-through and Kyle Burke blazed one way over the bar before the end.
Valley
Line-up: Liburd-Hines; Recci, Francis, Mace; English, Summerfield, Lee (Burke), Fitzharris, Sahota (Kear); Ahenkorah (Kirby-Moore), Wilson. Subs not used: McDonald, Motshweni. Bookings: Mace, Lee, Wilson. Sent off: Liburd-Hines.
