Andersson shot a 7-under 66 in a difficult wind on the Centenary Course to total 9-under 210 three hours before Wakefield finished his round.
Mark Warren (73) was a stroke back. Lee Westwood (69), Alastair Forsyth (72) and Phillip Archer (73) were next at 212.
Thomas Levet, who shared the second-round lead with Wakefield, was in the hunt until a double-bogey 7 at the 16th.
Colin Montgomerie shot 71 and was four strokes off the lead. Defending champion Paul Casey was another stroke back after a 73.
Wakefield went into the round after saying Friday he has had bad third rounds in the past.
'Without sounding negative, this is not expected,' he said. 'I'm disappointed with how I played today because after eight holes I was telling myself to hang on. But I made a good save from 12 feet on nine and a birdie from 10 feet on 10.'
He also birdied the long 12th, then after a three-putt bogey at the 16th and a drive into the rough at the last, he sank the 15-foot chip from the fringe.
'But I hit some very amateurish shots today,' he said. 'A 3-iron at the third I almost missed, and there were some others as well.'
Andersson moved up from 33rd place with a round capped by a 50-foot birdie putt at the short 17th. He also birdied the last hole, and there were two birdies from 20 feet and one from 15 feet.
'It was good to have no bogeys on my card,' Andersson. 'I have played solid all three days and I was able to get some putts in today.'
Warren, the first-round leader after a 65, had double bogeys at the fourth and fifth holes, but had four birdies on the last 11 holes without another dropped shot.
'It was a horrible start, with a five wood into the water at the second and out of bounds at the fourth,' he said.
Westwood was satisfied tee to green, but said the longest putt he holed was from 5 feet. He also missed from 18 inches at the seventh.