Town completed their perfect month of wins at the division's basement side, but they did make hard work of it at United's Second Meadow ground.
A combination of Valley's woeful finishing and an inspired display from home keeper Ollie Leslie made it an un-necessarily uncomfortable afternoon for Rugby, but three goals within the final twenty minutes made sure the hosts continue to look for their first point of the league campaign.
The visitors' starting line-up showed just one change from the Vase victory at Belper six days earlier, with Alex Lock in for Justin Marsden.
Biggleswade arguably edged the opening exchanges on a decent playing surface, but the pattern of the game was soon set when David Kolodynski was played through on goal by James Hancocks - only to put his chipped effort wide of the target.
Town then wasted a triple chance to open the scoring, with Lock first denied by Leslie before the same player hit the woodwork with his follow-up attempt, with Kolodynski blazing the next rebound over the bar.
Rugby continued to get in behind the susceptible United defence at will, but their finishing was often too elaborate.
Meanwhile at the other end, the hosts had a one-on-one opportunity of their own, but fortunately Jake Woodward was equal to Taylor Rhiney's effort, after the forward had run onto a long clearance.
Danico Johnson missed another good chance after Barry Fitzharris and Kolodynski had combined to set him up, before Edwin Ahenkorah finally registered one on 34 minutes when he swivelled in the box to fire home from twelve yards after Valley had initially pounced on a defensive slip-up.
The chances continued to come Town's way, with Kolodynski guilty of two misses in quick succession when first the ball stuck under his feet as he found himself in a threatening position and then he chose an deft dink over power to allow Leslie to make a save.
Ahenkorah was denied a second by a well-timed tackle by Marcus Wilson, and Loyiso Recci and Johnson both had headers kept-out by the busy Leslie - with Luke English hitting the bar in the same passage of play.
Woodward was equal to a further strike from Rhiney before the interval, with the home side making another good start to a half after the break - without really threatening the target.
A great double stop by Leslie then maintained Rugby's slender advantage, when he saved Lock's effort and then flung himself acrobatically to get his fingers to Fitzharris's shot from the edge of the area.
Johnson shinned one wide of the goal, before disaster struck for Town when Keenah Rosser was penalised for a foul in the box on Braima Fati to allow Rhiney to successfully stroke the spot-kick into the middle of the goal for the equaliser just past the hour mark.
Valley regained the lead on 73 minutes though, when Loyiso Recci headed home English's long throw, before Kolodynski and sub Dylan Parker spurned more chances to extend the advantage further when clean through on goal.
However having just seen his shot saved by Leslie, Johnson then grabbed Town's third when he scored directly from his whipped-in corner.
Kolodynski, Parker and Johnson were all guilty of missing further opportunities as the United back-line tired in the closing stages, but Johnson did find the net in stoppage time when he finished off Ahenkorah's cut back from the right hand side.
Valley Line-up: Woodward; English, Hancocks, Rosser, Loyiso Recci; Omar Recci, Fitzharris, Lock (Parker); Danico Johnson, Ahenkorah, Kolodynski. Subs not used: Bodycote, Clarke, Marsden, Francis. Booked: Fitzharris, Lock, Parker.
Biggleswade line-up: Leslie, Joyce, Ampadu, Andrews, Wilson, Puig-Vallis, Cousins, Hunt, Rhiney, Croucher, Fati. Subs: Newman, Ohabi, Otono.