Slough were on top in the first half, but were unable to test Rugby goalkeeper David Bevan. Rugby midfielder Steve Palmer was dismissed after picking up his second yellow card in a matter of minutes.
But Slough started the second period in terrible fashion, conceding seconds after the restart. Seb Lake-Gaskin ran at the Rebels defence and his weak shot squirmed past James Warrington at his near post.
Eight minutes later, Adam Logie sold Danny Murphy short with a pass, and the full-back brought down the lively Rugby striker Kolodynski when clean through on goal. Murphy's dismissal made it ten against ten for the remainder of the game, and the strike from the resulting free kick was spilt by Warrington into the path of Kolodynski, who scored.
Clearly shell-shocked by this, the Slough side, denied the services of Alex Brown, Stuart Swift, Nathan Bowden-Haase, David Deeney and Dominic Rhone through injury or suspension, was fortunate not to go three behind with Steve Perkins clearing another effort off the line.
But Slough rallied and after Bevan denied Jake Parsons with a brilliant save, the Rebels pulled a goal back on 72 minutes, Dan Burnell heading a chipped cross from Ed Smith just inside the far post.
Both sides missed good chances before Slough equalised on 82 minutes, Smith lobbing Bevan from fully 30 yards - the goalkeeper, clearly hampered by an injury, unable to backpedal quickly enough to prevent the ball dropping into the top corner.
Both sides pushed forward looking for a winning goal in the closing stages, but Rugby snatched all three points on the break as Slough were caught with players out of position. Kolodynski ran clean through and although Warrington saved his initial effort, the striker was able to tap home his second of the match to seal the win.
Rugby Town Line up
David Bevan, Alex Austin, Craig Kelly, Mason Rowley, Alex Gudger, Steve Palmer, Robbie Banks (c), Sam Youngs, David Kolodynski, Seb Lake-Gaskin, Fazel Koriya. Subs: Ed Booth, Jemal Wilson, Ellis Myles, Danny Hall.