Fisher's 63 set a new course record on the Heritage Course at London Golf Club.
David Frost and Graeme McDowell share third place at 7-under-par 65. Rory McIlroy is two strokes further back at minus-5.
Fisher played the back nine first and got his round going with back-to-back birdies from the 10th, then made two in a row again from the 15th to move to minus-4.
The Englishman stumbled to his lone bogey at the par-3 17th. He parred four straight around the turn.
Fisher, who tied for third at British Open qualifying earlier this week, caught fire on the fourth. He birdied the par-4 fourth and came right back with a birdie at five.
'It has been a tremendous week so far. Getting into another major is huge and gives you so much confidence,' Fisher stated.
At the par-4 sixth, Fisher drained his third straight birdie. He holed out from a greenside bunker for another birdie on seven, then kicked in a short birdie effort on the par-5 eighth to get to minus-8.
Fisher closed his round in style with a birdie on the ninth, his sixth straight birdie overall. Not only did he set a new course record, but he also established a new personal-best score on the European Tour.
'It was one of those days. The hole was as big as a bucket,' Fisher said. 'I got off to a great start with birdies on 10 and 11. To be honest, I kept my round going at 13. After chipping to about 20 feet, I made the par save. It just kept me going.'
McDowell parred four straight to start his round. After a birdie on No. 5, McDowell eagled the par-5 eighth. He ran off four birdies in a five-hole stretch from the ninth to get within two of the lead.
However, his birdie run was stopped by a bogey on the par-4 14th. McDowell atoned for that error with a birdie on 15, before he parred the last three holes.
'It was a tough day. The wind was blustery,' said McDowell. 'Eventually I got it going and 6 under par through a six-hole spell is always a nice way to boost the scorecard.'
Frost had a strong front nine with five birdies and four pars. He wrapped bogeys at 11 and 13 around a birdie on the 12th, then poured in three straight birdies from the 14th to grab a share of second.
Seven players are tied for fifth place at 4-under-par 68: Peter Hanson, Peter Hedblom, Jose Manuel Lara, David Lynn, Jeev Milkha Singh, Gonzalo Fernandez-Castano and Robert Rock.
Defending champion Colin Montgomerie opened with a 2-under 70 and is tied for 19th. Reigning British Open champ Padraig Harrington is among a large group tied in a 47th place at even-par 72.