The Australian blazed his way round the Blackstone GC layout in a nine under par 63 to climb from 19th overnight to establish a clear advantage.
The World Number 132's closest challengers heading into the weekend are Dane Søren Kjeldsen and Spain's Miguel Angel Jiménez, who shot 66 and 67 respectively to move to seven under.
Overnight leader Damien McGrane followed his opening 66 with a level par 72, and was joined by Rhys Davies and James Morrison in a share of fourth.
Rumford's effort was three shots better than anyone else has managed so far this week, and the 33 year old was on song from the start, landing four birdies in an outward 32.
After the turn he holed a 30 footer at the second, birdied 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, who picked up the last of his three European Tour titles in 2007. "It's a fickle game and it changes from week to week.
"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."
Despite a comfortable advantage, Rumford refused to look too far ahead when asked about the €367,500 winner's cheque.
"Well, look, it's anyone really that's within striking distance," he added. "I actually haven't looked at the leaderboard that closely, but as I shot today, there's nine under out there, so anyone that's within that seven, eight, nine shots back, you know, it's there.
"I guess after tomorrow we'll have a greater indication as to how it's going to unfold and how the scoring is going to go and how the course is set up. So just have to wait and see."
Like Rumford, Kjeldsen started the day only one under but birdied six out of seven holes from the 18th to the sixth to storm into contention.
"Got off to a little bit of a slow start and then when I caught fire, I kept it going," he said. "I think I made six birdies in seven holes I think, so I got it going so it was great."
Jiménez produced his usual array of brilliant iron shots in his seven birdie, two bogey round - no more so than at the last two holes.
He was within six inches at the 17th and four feet at the last as he finished his round on a high.
“I've been playing very well from tee to green,” said The Ryder Cup star. “And it's very good with my driver, consistent. Like you say, my irons, they are very good. Very nice iron shots to the green, and I'm giving myself many chances for birdies.
“I make only two bogeys in two rounds, but like you say, I've been hitting very solid my medium irons. That's the strongest part of my game normally when I'm playing well.”
His playing partner Lee Westwood is still in the hunt as well, after the World Number One shot a four under par 68.