The 35 year old, without a top ten finish on The European Tour this season, carded six birdies and a solitary bogey to share top spot on the leaderboard with playing partner Knut Borsheim.
“The consistency tee to green was steady,” said Rumford, whose last victory on The European Tour came five years ago.
“I just had one loose swing on 17, which cost me my only bogey of the day, so it was just a steady day.
“I guess I was just trying to be the best golfer I could be, and then twins came along, and now that's all changed and I'm trying to be the best father I can be. That's been really different the last couple of years.
“But I've got a great team behind me. I've got a great support in my wife, which makes things easier.”
Norwegian Borsheim had two holes in one as he came through Qualifying School last year, but has earned just four cheques so far in his rookie season and is outside the top 200 on The Race to Dubai.
Five birdies in a blemish-free round, including a pitch to four feet at the last, showcased the 25 year old’s talent, however.
“This season has been very new to me, all of the tournaments we are playing in and just the environment, you have to adapt I guess,” said Borsheim. “I've taken some time off now and just practicing with my coach, and it's back to scratch.
“I played solid golf - it could have been better; could have been worse, but a really solid round of golf and that's nice and gives you confidence for the next, because you're hitting good golf shots, hitting good chips and putts.”
Scot Paul Lawrie and Italy’s Francesco Molinari – the two confirmed members of Europe’s Ryder Cup Team playing this week - England’s Mark Foster, Dutchman Maarten Lafeber and Dane Thorbjørn Olesen finished the opening day one behind after all carded 68s.
Olesen enhanced his status as one of The European Tour’s rising stars by carding six birdies and two bogeys in a four under par 68.
“It's nice to see the practice has been paying off,” said the 22 year old. “I hit a lot of fairways and I'm still hitting the irons really good. I gave myself a lot of chances for birdie, so I was very pleased.
“It would be nice to follow him [Björn]. He's a big idol for me, so it would be really big for me to follow his footsteps. In Italy last year he gave me a little putting lesson and I shot ten under the next day, so it's probably the best advice.”
The display represents the latest in a string of eye-catching performances by Olesen, who claimed his first European Tour title at the Sicilian Open earlier in the year.
That was one of six top-ten finishes already this year, including a ninth-place finish at The Open Championship where he played with Tiger Woods in the third round.
“I got to see that my game is definitely good enough to be in a Major Championship and be up there in contention,” he added. “Obviously playing with Tiger and playing in one of the last groups showed that I can handle the pressure, also, and play well under big pressure, so I was very pleased.
“There were a lot of camera guys and a few bodyguards, and just a massive crowd. It was really special, and it was a great experience for me.
“My goal from the start of the year was to get in the top 20 in The Race to Dubai, and that's still my goal. It’s nice to move up in the World Ranking and it would be nice to move up a little bit more so I can get into the big events.”
Leading and selected first round scores in The European Tour's Johnnie Walker Championship at Gleneagles, Scotland on Thursday (GBR/IRL unless stated, par 72):
67 - Brett Rumford (AUS), Knut Borsheim (NOR)
68 - Francesco Molinari (ITA), Paul Lawrie, Thorbjorn Olesen (DEN), Maarten Lafeber (NED), Mark Foster
69 - Richie Ramsay, Richard Finch, Nicolas Colsaerts (BEL), Andrew Dodt (AUS), Victor Dubuisson (FRA)
70 - Chris Gane, Craig Lee, Chris Wood, Daniel Gaunt (AUS), David Howell, Gareth Maybin, Lloyd Kennedy, Thomas Bjorn (DEN), Benjamin Hebert (FRA)
71 - Joakim Lagergren (SWE), Johan Edfors (SWE), Emiliano Grillo (ARG), Marc Warren, Tommy Fleetwood, Bradley Dredge, Michael Hoey, Paul Waring, Matthew Nixon, Matthew Zions (AUS), Edouard Dubois (FRA), David Lynn, James Morrison, Ricardo Gonzalez (ARG), Tom Lewis, Gareth Wright, Andrew Marshall
72 - Andrew Johnston, Anders Hansen (DEN), Robert Coles, Scott Pinckney (USA), Peter Lawrie, Jose Manuel Lara (ESP), Felipe Aguilar (CHI), Joel Sjoholm (SWE), Alexander Noren (SWE), Rafael Cabrera Bello (ESP), Gregory Havret (FRA), Alex Haindl (RSA), Shiv Kapur (IND), Peter Whiteford, Greig Hutcheon, Colin Montgomerie, Richard McEvoy, Rhys Davies, David Drysdale, Andy Sullivan, Gregory Bourdy (FRA), Emanuele Canonica (ITA)
Selected:
73 - Shaun Micheel (USA), Tjaart Van Der Walt (RSA), Paul McGinley
74 - Scott Strange (AUS), Shiv Shankar Prasad Chowrasia (IND), Darren Fichardt (RSA)
75 - Darren Clarke, Marcus Both (AUS), Richard Green (AUS)
76 - Miguel Angel Jimenez (ESP), Jbe Kruger (RSA)
77 - Dylan Frittelli (RSA)
78 - Jose-Maria Olazabal (ESP), Rich Beem (USA), Keith Horne (RSA), Marcus Fraser (AUS)
82 - Michael Campbell (NZL)