Valley dug deep to see off lowly Rothwell, with Charlie Evans's 63rd minute winner securing them the points at Butlin Road.
Richard Blythe had headed Town into a half-time lead, but the resolute visitors gave them a shock eleven minutes into the new period with an equaliser before Evans also scored with his head to extend Rugby's recent winning run to five matches.
Lewis Hayden came back into the starting line-up in place of the suspended Dom Perkins, with Josh Steele and Fazel Koriya preferred to Trey Brathwaite and Stefan Blake in two other changes from the previous weekend's victory at Pinchbeck.
The hosts dominated possession throughout the first half, although it was Corinthians that had the game's first chance when Ade Ademidun headed wide from a corner.
A Liam Francis volley on the turn - also from a corner - was Town's first attempt on goal shortly after, with Danico Johnson then dragging a shot wide after Lewis Rankin's lofted pass had picked him out in the box.
Koriya lifted one into the arms of away keeper Martin Thorpe, ahead of the game's opener on 25 minutes when Rankin's free-kick smacked back off the crossbar and Blythe followed up to loop his header over Thorpe into the net.
Rankin twice sent efforts comfortably off-target before the half-time whistle ended what was at times a sloppy and over-elaborate opening 45 minute display from the home side.
The new half started with Blythe shooting over and Evans heading Steele's cross straight at Thorpe, before Rothwell's Aiden Smith looped a cross over the head of Valley keeper Matt Hill to stun the home fans.
Rugby responded well to the setback though, and appeared to step up a gear straightaway, with Evans helping the ball into the side netting, after Johnson had headed Keenah Rosser's cross back into his path.
A previously unusually subdued Johnson then muscled his way past a couple of defenders on the byline to chip a perfect ball across to Evans - who this time made no mistake with a finish into an unguarded net.
A further Johnson delivery was soon playing in Koriya, but Thorpe did well to keep out his strike with a low save.
Ryan Clark's speculative effort from distance which bounced wide and Ademidun's wayward free kick were the closest the visitors came to another leveller, whilst a well-executed mid-air volley by Johnson and a dinked effort from the edge of the penalty area by Town sub Harry Holloway both narrowly missed the target ahead of the end of the game.
Line-up: Hill; Rosser, Steele (Brathwaite), Recci, Francis; Blythe, Hayden (Holloway), Rankin; Koriya, Evans (Tulloch), Johnson. Subs not used: Blake, Kavanagh. Booked: Johnson.
Rothwell line-up: Thorpe, Smith, Phillips, Plowright, Campion, Nugent, Healey, Johnson, Ademidun, Clark, Gillard. Subs: Wright, Ogazi, Nugent, Rice.