Currently 173rd and 203rd in the Official World Golf Ranking respectively, the pair are one clear of four players -.Thailand's Chapchai Nirat, Dane Jeppe Huldahl, Argentina's Ariel Canete and Dredge's compatriot Phillip Price all managed to shoot 65.
Dredge set the early target after turning in 33, making an eagle on the long 11th and then finishing with three birdies in a row.
The 36 year old, whose last European Tour win came four years ago, said: "There was virtually no wind and the course was probably the easiest I've ever played it.
"I'm surprised there were not more low scores. It's a matter of consistency at the moment - when I play well I play very well, but on an off-day it's a mid-70 round, which isn't going to to do you any good."
Whiteford graduated from The Challenge Tour for a second time at the end of last season, but has almost done enough already to secure his card for next year and was a runner-up in Malaga in March.
The 29 year old, who eagled the 481 yard sixth and kept a bogey off his card just like Dredge, commented: "It sounds stupid, but I'm not swinging it that great.
"I was terrible in practice and it was a bit of a struggle to be honest, but sometimes that's when you play your best golf.
"When you are not 100 per cent confident you don't take on the flags and that's kind of what I was doing. It paid off."
Past and present Ryder Cup Captains Sir Nick Faldo, Bernhard Langer and Colin Montgomerie are all in the field and while the last two shot 70 Faldo managed only a 76 in his first event since last year's Open Championship.
"It's just scary," said the six-time Major winner, who decided on the event as a warm-up exercise for The Open Championship at St Andrews in three weeks.
"I didn't make a follow-through on the front nine, but I felt a bit more comfortable after that."
Huldahl, who hopes the Danish football team can make it a "great day" by beating Japan at the World Cup this evening, commented: "I feel like I've been playing better than the actual results lately so I'm just trying to push on and hopefully it will come."
Canete, who is on a medical exemption after problems with shoulder injuries, was delighted with his return to form.
"I played consistently, and the putter was very good today," he said. "So comfortable, a nice day."
Ernie Els, third in the US Open Championship at Pebble Beach last Sunday, bogeyed the last two holes for a 70, while World Number Eight Paul Casey returned a 68.