Valley recorded a second straight away league win, thanks to two second half goals from David Kolodynski and Dylan Parker in Cambridgeshire.
It was a largely one-sided affair at the sun-drenched Bearscroft Lane ground, with the visitors missing out on the chance of a more emphatic margin by squandering a number of gilt-edged chances.
There was a single change to Town's starting line-up from the victory at Long Buckby four days earlier, with academy prospect Melu Mpande preferred at left-back to Lee Thomas.
With the wind and a slope in the favour, Rugby looked to make an early breakthrough, but the first opportunity of the game actually fell to the hosts when Matthew Allan dragged one wide from an angled position.
However Town were soon creating a flurry of chances of their own, with Danico Johnson's powerful effort parried by home keeper George Whitehall and both Kolodynski and James Hancocks both failing to capitalise on loose balls in the box.
Danico was soon finding himself through on goal, but his mis-controlled chest down saw the ball run too far ahead - allowing Whitehead to gather.
The in-form Valley striker continued to torment the Rovers' back-line though, and his fizzed cross was just missed by Barry Fitzharris, before the ball was finally scrambled away by a desperate home defence.
Max Johnson's ambitious shot from distance was comfortably taken by Whitehall, before another Rugby striker found a clear path through the middle - but this time it was Parker's turn to fail to gain proper control and he ultimately shot wide.
A Kolodynski speculative strike flew just over, as the opening period drew to a close.
The second half continued in the same manner, and it was only three minutes old when Rugby took the lead after Kolodynski poked home Danico's cut-back from the left.
Town looked keen to increase their lead, and Kolodynski's dipping strike was again inches high of the frame following an impressive spell of possession by the visitors.
Whitehall kept out Danico's strike, after he had shown good skill to beat his man, with Parker then flashing a cross dangerously across the face of the goal.
It was two-nil on 72 minutes though, when Hancocks and Kolodynski combined well to release the marauding Keenah Rosser down the right hand channel, and his squared pass fell nicely for Parker to complete another straightforward tap-in.
Parker had two further half-chances, but his final shots were both off-target, with Town substitute Justin Marsden almost adding a third - only to be thwarted by the busy Whitehall.
The hosts did twice go close in the game's closing stages though, with first Ben Newey pulling off a fine point-blank stop to keep out Allan's effort, before Mike King struck the angle of the frame after he had connected well from twenty yards.
Line-up: Newey; Rosser, Mpande, Loyiso Recci, Francis; Hancocks (Lee Thomas), Max Johnson, Fitzharris (Marsden); Parker, Kolodynski, Danico Johnson (Revan). Subs not used: Hayward. Booked: None.
Godmanchester line-up: Whitehall, Zequiri, Augusto, Moss, Chadwick, Munro, M.King, Dickerson, Allan, Unwin, Wills. Subs: Cobb, Radwell, R.King.