Dredge, the leader after Thursday's suspended first round, shot 3-under-par 68 in Saturday's third round, while Rumford moved into a share of the lead with his second straight 5-under 66. Their 54-hole totals are 13-under 200.
"I felt my 68 was a bit mediocre because I made some bad errors," Dredge said. "But I've not been playing well for the last month or so (and) you have to turn your form around sometime."
In Sunday’s final round, Dredge will bid for the third victory on the European Tour.
Oliver Wilson (70) is third at 12-under 201.
Dredge, Rumford and Wilson comprised Saturday's final threesome, and two members of the trio were among the walking wounded.
Wilson had a left shoulder injury, and Rumford needed treatment for a severe headache.