Both leaders had six birdies and a bogey in windy conditions at the Doha Country Club. Robert Karlsson, Alexander Noren, Marcel Siem and Lee Westwood are tied for third at 4-under 68 and Brett Rumford is alone in seventh at 3-under.
Charl Schwartzel, who won the last two weeks and is seeking to be the fourth player to win three consecutive European Tour tournaments, was at 2-under 70 and tied for eighth.
Dredge, playing the back nine first, opened with a bogey and was even on the day after 11 holes. He had a birdie at No. 3 and consecutive birdies on Nos. 5-7 before a closing birdie gave him a share of the lead.
Wilson had a bogey between birdies at Nos. 2 and 4 and moved into first with four birdies in a seven-hole stretch. He closed his round with five straight pars.