In the sixth minute Potton took the lead when a shot from Calum Forster was saved by the keeper, only for Danny Webb to net the rebound.
The advantage was doubled six minutes later when a centre from Webb was turned into the net by the industrious Aidy McClean. Luke Harradine had a header blocked and Piesse headed over from close range.
Potton continued to apply pressure and Forster saw his fierce shot from 25 yards rebound from the cross before Cooper missed an easy chance. It was all Potton and from James Meredith’s centre Webb headed wide.
Just before half-time a high centre from Cooper hit the top of the crossbar and bounced out of play.
Biggleswade Town outline aims to bounce back at the first attempt
Biggleswade Town and Biggleswade FC to get under way but United exit FA Cup
Fishing report: Terry's successful at Broom Lake
Biggleswade clubs all in action as United boss Cristian Colas braces for league opener
GUILLEM BALAGUE: We're so proud to be part of the Biggleswade community
The one question mark was whether Potton would rue missed chances but those fears were allayed in the first minute of the second half when Meredith played in Chapman who chipped it over the keeper to make it 3-0.
In the 56th minute Potton increased their lead when a cross from Piesse was tapped into the net by Webb. Five minutes later several attempts by Potton were blocked in the six yard box before Meredith added the final touch for the fifth.
Van Tonder was just wide with his header and then at the other end Webb had a good run only to be thwarted by a good save.
Potton introduced new signing Sam Leonard who came on for the last 30 minutes and settled in well as a central defender.
Kenny Smith also came on as substitute but sustained a recurring leg injury and had to leave the field leaving Potton with 10 men for the last 10 minutes.
Credit to Oakham for not giving up and playing clean football. Potton host Melton on Saturday.
Potton United: Will Cook, Calum Forster, Charlie Stafford. Shaun Faulkner (Sam Leonard), Luke Harradine, Aidy McClean (Kenny Smith), Danny Webb, James Meredith, Matt Chapman, Cory Cooper (Nick Finney), Sam Piesse