Dredge fired nine birdies and one bogey at Kungsangen to finish 13 under par, one clear of England's Barry Lane and Sweden's Pierre Fulke.
Swede Henrik Nystrom and France's Jean-Francois Remesy are a shot further back on 11 under.
The forecast for the weekend predicts more of the heavy rain which forced Wednesday's pre-tournament pro-am to be cancelled, and Dredge was well aware of the possibilities.
"The golf course would not be able to take much rain and my caddy and I discussed it beforehand," said Dredge, whose previous tour win came after he shot a third-round 60 in the Madeira Island Open in 2003.
"We knew there was a chance if we have some thunderstorms we might not play on the weekend so we wanted to go as low as possible. Twelve under was the target and we've got to 13 which is great."
Bad weather also affected last week's Deutsche Bank Championship with the first day's play washed out entirely.
Dredge carded a third-round 69 to lead by two shots after 54 holes, but could only manage a closing 73 to finish three behind eventual winner Niclas Fasth.
Lane carded seven birdies to add a 66 to his opening 64 in his 533rd European Tour event. The 45-year-old, who went 10 years without a win before claiming the British Masters title last year, would have shared the lead but for driving into the lake to the right of the 15th green to run up one of his two bogeys.
"I had a terrible lie on the 15th tee, it was on one of those tee pegs," joked the former Ryder Cup player. "I thought it might miss the water it was so far right but I'm happy with the way I played overall. I shot 64 in the first round and came to the golf course to find myself six behind so I've not done too bad."
Fulke qualified for the 2001 Ryder Cup later postponed for a year with victory in the Volvo Masters and second place in the World Matchplay in Melbourne, but now concentrates more on his course design business than tournament golf.
"I have got a lot of projects going on," said the 34-year-old after matching Dredge's 63 with eight birdies. "I took eight weeks off after finishing third in Qatar to deal with them and then play golf in the summer.
"It works well. I haven't done anything properly the last couple of years, including my golf, so I've tried something different this year to see if it works. Now that I focus on the right thing, each week I come out it gets better and better. I think I'm playing better than ever."
Pre-tournament favourite Adam Scott is six shots off the pace on seven under, the world number seven adding a 65 to his opening 70.
With the course shortened by 386 yards due to the wet conditions, low scoring was the order of the day and the cut fell at four under par, last week's winner Niclas Fasth missing out by one after a double-bogey seven on the 17th.