Donaldson led the way after rounds one and two but slipped to a share of second place when he shot one-under-par 71 yesterday. Dredge fired 66 for a 12-under total of 204 which sees him lead by two from his fellow Welshman and Denmark's Soren Kjeldsen (68).
However, Donaldson need only finish in the top seven to claim the €30,000 he requires to secure his place at Gleneagles with one tournament - next week's Italian Open - to spare. Scotland's Stephen Gallacher, also hoping to make Paul McGinley's Europe team, remained in the top five at the Albatross Golf Resort ahead of the final day.
He dropped two places after a 71 to share fifth spot with South Africa's Merrick Bremner on eight under, one shot adrift of France's Gregory Bourdy.
Gallacher said: "I would have liked to have been a couple of shots better off, but I struggled a bit on the greens, though I still shot under par which was nice.
"I'll just try to shoot as low as I can and see what happens at the end of the day."
Donaldson could still make McGinley's team via the world points list should he fail to enhance his bank account enough over the next nine days, but qualification via the European route would come as a relief, with Graeme McDowell, Ian Poulter, Luke Donald, Gallacher and Joost Luiten all battling to qualify that way.
Missing the cut at The Barclays will have put a major dent in Poulter and Donald's chances of making the team that way, but McDowell is still involved in New Jersey.
Donaldson admitted he should have tightened his grip on the lead in Prague but made too many errors. He said: "It was there for the taking today for me to extend my lead but I made too many sloppy mistakes.
"I've played a lot of golf recently. I'm not too fatigued, though. I probably will be when it's finished but the adrenaline just keeps you going through the event if you're doing well."
The 38-year-old threatened to run away with it when he eagled the first and picked up another shot on four to move to 12 under, but he could not find consistency and a bogey on the next was followed by a run of birdie, double-bogey, birdie on seven, eight and nine.
Another birdie followed on 12 but bogeys on 13 and 18 meant he picked up just one shot over the day. Dredge, by contrast, was faultless picking up birdies on five, nine, 11, 12, 14 and 15 to move him into the lead.
"I've had no bogeys since the first day and it's nice when you do that," he said. "All the birdies count then and I've been delighted with the last two rounds so if I can do that again tomorrow I would be over the moon.
"It's nice to be up at the top and contending again at this tournament, it's what all of us guys practise for and I'm enjoying it so hopefully I can have a good round again tomorrow."
Craig Lee and Paul Lawrie are the next-best-placed Scots. They are among nine players in a tie for 17th after both carded 71 yesterday.