The 33 year old led the way at ten under overall, with Denmark's Søren Kjeldsen - who had started the day alongside Rumford at one under - shooting a 66 at Blackstone GC in Icheon to take second in the clubhouse.
Englishman Richard Finch had worked his way alongside Rumford with eight holes still to play, completing the first ten in five under par.
Rumford, who won the last of his three European Tour titles at the Omega European Masters in 2007, teed off at the tenth and claimed four birdies going out before hitting top gear on the way in.
He holed a 30 footer at the second, from 18 feet at the next, then almost holed his approach at the fifth - leaving a tap-in birdie - with further gains at the sixth and eighth .
"I haven't come into this week with that great of form technically but this is a funny game," said Rumford. "It's a fickle game and it changes from week to week.
"So I guess the last two weeks, not playing so well, I've just been really grinding every round out. And I guess it's striking a little better this week and rolling my putter nicely as I've done the last two weeks.
"I guess, just the hard work over the last couple of weeks to grind and get myself into the scoring mentality rather than anything else has helped for this week. I just need to stay in the same frame of mind and see where it takes me over the weekend."
World Number One Lee Westwood made steady progress to reach the turn three under par, but was still seven off the pace.
Opening-round leader Damien McGrane of Ireland, who shot 66 on Thursday, played his first seven holes in two under to close the gap on the leading pair to two.
Welshman Rhys Davies had improved to six under after a four under par round, and was joined by England's James Morrison (69).
Finch slipped back to seven under when his ball was lodged in a tree at the 12th, leading to a triple bogey.