With Wing Back Jonny Hale out injured, Ross Brock was moved out to the left and was accompanied by Harry Mohide, James Parsons and Finn Hardy in defence.
After a nervy first 20 minutes, neither side could score the opener even though there were several chances at either end. It was Carter Box who eventually opened the scoring from a freekick just outside the box which somehow outwitted the Swiss Valley Keeper.
Before the break Taylor Aspinall made way for Harry Beresford; both of which put in a decent performance in midfield.
After the break, Lucas Coppin added a second which only just sneaked over the line thanks to a fumble from the Keeper. This goal proved to be decisive as Swiss Valley scored moments later from a few yards out leaving Keeper Tom Turek helpless.
Chances fell to Iestyn Essery, Adam Woolley and Lewis Magor late on but none could be converted and Pumas held on to continue their 16 match unbeaten streak.
Pumas now face Locking in the Second Round of the cup next weekend.