Town eventually ran out comfortable winners against relegation threatened visitors in front of a bumper free-admission Butlin Road crowd of 450.
A Dom Perkins double had given Valley the lead, but having then seen their advantage reduced, the hosts survived a number of scary moments either side of the interval before further strikes from Lewis Rankin and Fazel Koriya settled things against a team who ended the game a player light.
Matt Hill was back in goal for Rugby after a one-match absence, whilst there was a debut for new signing Dan Summerfield and a return for Richard Bunting in midfield for the first time in three months.
Town made a purposeful start for a change, and could have taken an early lead when Keenah Rosser finished off Edwin Ahenkorah's cross but the official's flag meant it was chalked off.
Summerfield's shot from distance was well-gathered by Muxloe keeper Ashley Marsden, before the deadlock was broken when Perkins scored on the turn at close quarters after Liam Francis had struck Rankin's corner onto him.
The visitors were then awarded consecutive free-kicks on the very edge of Rugby's box. However the first saw a Kirby infringement in the defensive wall and Remell Davis blazed the other one way over Hill's goal.
Town's second came when Perkins was once more on hand to bundle home Koriya's cross from the left on 38 minutes - with Francis again providing the final assist.
Andre Williams was soon reducing the arrears though with a neat curled finish after cutting inside from the right, and Kirby could easily have been level at half-time when they were awarded a free-kick inside the area this time after an adjudged Rugby back-pass.
However the visitors' skipper Adam Parry smashed the ball against crossbar after the set-piece was tapped back to him.
The new period was only a couple of minutes old when Davis got in behind the Town defence, but Hill pulled out a decent save to deny him.
From the resulting corner, Valley somehow managed to protect their lead from a protracted goalmouth scramble which saw two further good stops by Hill and a number of other blocks from his team-mates.
Rankin settled any Rugby nerves on 53 minutes though, with a composed strike past Marsden to maintain his rich scoring form of late.
Summerfield blazed one way over as Town upped their gear, and the dismissal of Tyler Love for an off-the-ball stamp on Perkins created an even wider gulf between the two sides.
Loyiso Recci had what appeared to be a perfectly legal header ruled out for offside, and Perkins just missed out on his hat-trick when his rising effort from thirty yards clipped the top of the woodwork.
Town grabbed a fourth though after sub Harry Holloway's exquisite volleyed crossfield pass picked out Ahenkorah and his centre into the box was helped home by Koriya.
Marsden then saved Ahenkorah's goalbound strike to keep the final margin down, with Rankin and Ahenkorah also both going close in the final stages of the match.
Line-up: Hill; Recci, Francis, Perkins (Kavanagh); Rosser (Holloway), Koriya, Summerfield, Bunting (Steele), Rankin; Evans, Ahenkorah. Subs not used: Connor, Tulloch. Booked: None.
Kirby line-up: Marsden, Clarke, Morrall, Mangham, Finnemore, Williams, Parry, T.Love, Tinsley, A.Love, Davis. Subs: M.Love, Robinson, Squires.