Valley dug deep to win narrowly at Cogenhoe United and claim a tenth straight league victory.
Rugby took an early lead through Jordan Wilson but the hosts scored a deserved equaliser just before the interval.
Town then rode their luck a little at times during the second half, but they managed to snatch all three points thanks to Caine Elliott's seventh goal of the season on 72 minutes.
Ben Whitehead made his first league start of the campaign in one of three changes from the weekend win at Lutterworth, with Alex Lock and Luke English also on the pitch from the off.
The first chance of the cold evening fell to Cogenhoe, but English was back well to execute a blocking tackle on Jessi Obeng after the winger had found space in behind the Valley left hand flank.
However there were less than five minutes on the clock when the visitors broke the deadlock, after Ryan Seal's wind-assisted ball forward fell to David Kolodynski - who in turn laid it onto Elliott for a strike at goal.
Home keeper Ben Heath could only parry Elliott's effort into the path of Wilson, who duly helped the rebound home.
Louie Barrett fired one way over the bar and then Town keeper Matt Hill did well to deny Jamie Hall after the United striker had been played through for a one-on-one by Obeng, as the hosts looked to get back on level terms.
However Rugby then put in their most threatening spell of the game - creating a number of scoring opportunities in the process. Kolodynski should have done better with his connection to an Elliott pass, and then the same player failed to get a shot off in an equally dangerous position.
Wilson twice failed to take full advantage of two chances created for him by Seal, before he wasted a further golden opportunity with a weak shot straight at Heath after Elliott's cut-back found him unmarked in a central position in the box.
Heath was then down well to keep out a bobbling effort by Kolodynski, with Liam Francis glancing an English long throw wide and Wilson also mis-hitting Kolodynski's delivery after Rugby had broke quickly upfield.
Rugby were made to pay for their wastefulness on 43 minutes when Barrett's low cross was just beyond the reach of Hill - allowing Hall to slide in at the back post and find the net.
There was more bad news for Town ahead of the break when Dan Summerfield was taken out with the final kick of the half and was ultimately stretchered off during the half-time interval with a foot injury.
Cogenhoe made the better start to the new period, and really should have edged ahead when a ball ricocheted nicely into the path of Obeng - leaving him just Hill to beat. Not for the first time on the night though a Cogenhoe forward wasted the opening and could only poke the ball wide of the post.
Obeng then tested Hill with a low shot, before Town finally threatened at the other end when Heath tipped over a teasing cross from the right by English.
Barrett almost got in again behind an at times worryingly open Valley defence, ahead of what proved to be the game's decisive moment which came when Town sub Madundo Semahimbo showed tricky feet to make inroads into the United box before his strike rebounded nicely for Elliott to power home.
The game became increasingly tetchy as it neared its conclusion, although Town generally coped well with the home side's efforts for another equaliser late on.
Luca Purse had a couple of headers that failed to trouble Hill to any great extent and Cichosz also put one wide, as Rugby held on for their eighth away league success of the season.
Valley Line-up: Hill; Francis, Whitehead, Recci; English, Summerfield (Ahenkorah), Lock, Elliott, Seal (Fitzharris); Wilson, Kolodynski (Semahimbo). Subs not used: Kear. Booked: Lock, Hill, Elliott.
Cogenhoe line-up: Heath, Tsinosis, Ansell, Parkes, Purse, Romayne, Barrett, Cichosz, Hall, Weatherly, Obeng. Subs: Briggs, Waple-Moors, Snapes, Going, Anderson.