BEIJING, May 4, 2013 (AFP) - Rumford, 12 under in the $3.2 million OneAsia tournament, was helped in part after Finland's Mikko Ilonen (73) blew his share of the lead with a bogey on the last after his tee shot found the water.
Spain's Pablo Larrazabal (69) was third, a shot further behind, while Thailand's Kiradech Aphibarnrat (72) found his putter turned cold and was alone in fourth at nine under.
Rumford, who ended a six-year drought on the European Tour with victory at the Ballantine's Championship in Korea last week, missed six greens during Saturday's round, but scrambled par each time.
"That was a tough day, a really tiring day, I really started to feel it on the back nine," Rumford said in a OneAsia press release.
"I was fortunate enough to make some good up and downs today, but a lot of the areas where I was missing it were seemingly pretty easy to get up and down."
Ilonen started with a bogey that he repaired on the next hole and did the same again at six and seven before parring everything until the last.
"Overall I still played pretty well, I just didn't give myself enough birdie chances," he said, "but I hung in there nicely, and I've still got a good chance tomorrow.
He described the day's play at the Tianjin Binhai Lake Golf Club as a "good fight", adding he would have to play very well to beat Rumford on the last day.
France's Victor Dubuisson made the biggest charge of the day with a 66 that lifted him to a share of sixth place at seven under, with first round leader Robert-Jan Derksen (73).
Teenage amateur Dou Zecheng put in another excellent performance, finishing the third round with a level par 72 to stand two under for the tournament.
Dou, 16, made it into the tournament via regional qualifying and was the only amateur to make the cut -- as well as the youngest in the event's 19-year history.
"I had some good iron shots and my putting was especially good today, but I still need to improve on my distance," he said.
Scores after round three of the Volvo China Open 2013:
204 - Brett Rumford (AUS) 68-67-69.
205 - Mikko Ilonen (FIN) 69-63-73.
206 - Pablo Larrazabal (ESP) 71-66-69.
207 - Kiradech Aphibarnrat (THA) 68-67-72.
208 - Joost Luiten (NED) 73-67-68.
209 - Victor Dubuisson (FRA) 71-72-66, Robert-Jan Derksen (NED) 66-70-73.
210 - Ricardo Santos (POR) 70-72-68, Park Sang-hyun (KOR) 69-70-71.