Town had to come from behind to see off the division's bottom club at a windswept London Road, as they were once more made to work hard for their victory.
Playing against the strong gusts Valley had gifted the hosts the lead on the half hour mark, before two goals within four second half minutes from Keenah Rosser and Edwin Ahenkorah secured them the points.
Rugby boss Carl Adams made one change from the impressive win at fellow title challengers Deeping the previous week, with Josh Steele making his tenth start of the campaign in place of the rested Dom Perkins.
Despite a bobbly pitch further diminishing the prospect of a good footballing spectacle, Town started well enough and were soon creating chances to open the scoring.
Charlie Evans should have done better early on when he outpaced his marker to race onto a ball over the top of the Whitworth defence, but his final effort lacked conviction and was easily taken by home keeper Adam Honour.
However Honour was soon spilling a Rosser cross after a neat back-heel by Ahenkorah, with Lewis Rankin unable to convert the rebound.
Evans did then head Loyiso Recci's cross against the angle of the goal frame, with the home side scrambling the ball away for a corner.
Wellingborough scored straight the subsequent Valley set-piece though, after Recci and Simeon Tulloch both left the ball to each other outside the hosts' penalty area and from the resulting counter attack Remy Brittain placed his cross on the head of Ben Mason to nod into the top corner.
Rugby pushed for an equaliser ahead of the half-time interval, with Recci's head down to Rankin's corner just eluding his team-mates, before Liam Francis flicked one wide.
An Ahenkorah cross was also narrowly beyond the reach of its target and a Justin Marsden strike from the edge of the box flew over the bar in the period's closing exchanges.
Town dragged themselves back level ten minutes after the restart though, when Honour flapped at a deep cross by Steele - pushing the ball straight onto Rosser's head, who duly helped the ball home.
Marsden then fired in another effort from twenty yards, and this time Honour was forced to tip it over.
The corner that followed from Rankin was met by Recci at the back post and he headed the ball across to Ahenkorah for a straightforward finish to give the visitors the lead.
With the wind now behind Rugby's backs, it was pretty much one way traffic from there on in, but they were unable to ram home their advantage with further goals.
Ahenkorah nearly grabbed his second when he beat Honour to a long kick upfield from Town keeper Matt Hill, but his effort was blocked, and Francis again missing out with a near post chance.
A strong penalty claim for a foul on Francis was turned away and Evans squandered another one-on-one opportunity, whilst Rankin twice tried his luck from distance with no success.
The home team's hopes of snatching an unlikely late equaliser all but disappeared when they were ultimately reduced to nine men late in the game, with Connor Jameson and Ashley Hunt both receiving their marching orders for second yellow cards within a few minutes of each other.
Evans headed one wide between the two sending-offs and Honour was at full length to keep out a decent strike from Steele in the two final chances of the game.
Line-up: Hill; Recci, Steele, Francis; Rosser, Tulloch, Summerfield, Marsden, Rankin; Evans, Ahenkorah. Subs not used: Kavanagh, Perkins, Connor. Booked: Evans, Marsden.
Wellingborough Whitworth line-up: Honour, Codrington, North, Ward, Purser, Hunt, Brittain, Massaro, Mason, Jameson, Giles.