Jonny Franks went on to complete a hat-trick while Harry Roach also weighed in with a brace.
Danny Lewis completed the scoring to leave player-manager David Seligman purring over his second-half display.
He said: "In the first-half we were okay, but in the second half we showed our class despite some of our players being missing today.
"Oakhill are a much-improved team, but in the end we had too much quality. We are annoyed to have conceded a sloppy goal, but are looking impressive in both defence and attack.
"Our next opponents will know they’re in for a tough test."