After Dave Woozley had headed an early Stuart Swift free kick wide, Seb Hamilton stroked home the first with just six minutes played, after the striker had brought the ball forward and skipped past a Slough challenge with ease.
It could have been two just minutes later, but Luke Keen, on his return to the Rugby line-up, headed a cross from fellow debutant Robbie Banks just wide.
Slough went on to have good chances, despite not being at their fluent best. Stuart Swift tested Valley goalkeeper Louis Connor with a free kick, and he then denied Sean Sonner superbly in Slough’s best spell of the half.
The visitors had a goal rightly ruled out for a foul on Connor as Slough looked to capitalise on the swirling wind from a corner kick.
But nine minutes before the break, the hosts again capitalised on poor Slough defending, Luke Keen getting past his marker far too easily and blasting past an exposed Warrington.
Despite having large spells of possession in the second half, the hosts held firm as Slough were unable to muster any more meaningful attempts at Connor's goal. Rugby started the half on top, and blasted an effort well over, whilst Sonner headed a Swift cross wide, the striker having more time than he realised.
Both Banks and Keen went close for the home side in the second half, with Slough substitute Charlie Mpi twice denied a late consolation – first by the legs of Connor and then by a brave saving tackle by Lee Miveld.
Dangerman Keen beat Warrington again towards the end, but was denied by a linesman’s flag to frustrate Rugby.
Slough tried in vain to create a chance, but could not turn their considerable ball possession into a goal, and Sinclair could only hit Burnell with an effort from distance, the ball trickling wide.
Rugby stood firm and the Rebels left Butlin Road frustrated once again, having lost 1-0 in the same fixture last season.
Rugby Town Line up
Louis Connor, Gary Moran, Jemal Wilson, Robbie Banks, Melvin Gourlay, Luke Keen, Ben Steane, Lee Miveld, Tyrone Fagan, Seb Hamilton, Richard Wesley. Subs: Andy Gundelach, Adam Khan, Lynval Da Costa, Steve Evans, Ryan Isherwood.