Pugh, a forgotten man this season in the first team, started the game as he netted from Nick Gray's cross to break the deadlock with only 12 minutes remaining.
Leeds were not fully tested by Rodez as the home side created their opportunities mainly in the second half.
Leeds were followed by around 300 travelling fans and Kevin Blackwell said they were amazing. "The French could hardly believe how many we had brought over here," he said on the official Leeds website. "They were singing all night long and everyone at Rodez has told me how impressed they were with them.
"The owner of Rodez is a very ambitious man and I am pleased for him that it was a very close game, at times they did very well. We gave the likes of Danny Pugh, Nick Gray and a few other lads whose contracts are up soon a game so we take a closer look at them and they did well."