Kenneth Ferrie fired a 5-under 67 to climb to 7-under-par 137. He shares third place with Ian Woosnam (69), Robert Rock (68) and Soren Hansen (68).
Clarke struggled on the front nine during his round. He bogeyed the par-4 first but recovered that stroke when he birdied the par-5 fourth. However, the Ulsterman dropped another shot when he bogeyed the par-4 seventh.
The nine-time winner on the European Tour caught fire on the back side. He notched back-to-back birdies from the par-5 12th and tallied another pair of birdies from the 17th to close at minus-9.
'I played well again,' said Clarke. 'I had numerous chances everywhere and I'm pretty pleased with a 69. The wind was gusting and that's a pretty good score. I was hitting the edges of the hole all day and I am certainly playing well enough to be doing well in this tournament.'
Through the first two rounds, Clarke is minus-5 on the 17th and 18th holes combined.
'My patience is being severely tested at the moment, severely tested,' Clarke said. 'But that's what happens. I have to keep on playing the way I have been and hopefully my scores will get better.'
Fasth also opened with a bogey at the first hole on the West Course at the Wentworth Club. He atoned for that mistake with a birdie at the fourth and later rolled in another birdie putt at the par-4 eighth.
Around the turn, Fasth continued to play well on the par-5s as he birdied the 12th. The Swede ended his round in fine fashion with birdies on each of the final three holes, two of which were par-5s. Two of those putts came from within three feet of the cup.
Fasth credited his par-saving putt on No. 15 as one of the big keys to his round.
'Sometimes you feel when a par putt goes in, it's really, really important. I holed a good one on 15, to sort of stay with the pace,' said Fasth. 'That felt really good. I felt that was one of the big moments, just making a simple seven-foot putt.'
Ernie Els and Trevor Immelman each shot rounds of 3-under 69 to move into a tie for seventh at 6-under-par 138. Gordon Brand, Jr. and Alastair Forsyth are also at minus-6.
Defending champion Anders Hansen is among a large group tied at 2-under-par 142.
The cut line fell at minus-1. Among those failing to make the weekend were Retief Goosen and Paul Lawrie, both at even-par 144.