Oliver Wilson posted a 65 to take third place at 13-under-par 131. Jarrod Moseley and Simon Nash were one shot further back at 12-under-par 132.
Fasth only had three birdies in a remarkable round at Gulf Harbour Country Club. He picked up his first birdie of the day at the par-5 second and took advantage of the other par-5 on the front nine with an eagle at the sixth.
The Swede then eagled the par-5 11th and followed that up with an incredible eagle at the par-4 12th when he holed out from a bunker. Fasth added a birdie at the par-3 15th and another at the par-5 17th to secure the 36-hole lead.
'You have to believe in what you are doing,' said Fasth. 'If you get down on yourself it takes more to turn it around.'
Tunnicliff birdied the second but gave that shot back with a bogey at the fourth. He responded in style starting with a birdie at the par-4 fifth that he followed up with an eagle at the very next hole.
The Englishman then birdied the seventh and the eighth and ran off back-to-back birdies from the 10th to reach 12 under. Tunnicliff closed his round with back-to-back birdies from the 17th to take the clubhouse lead at 14 under until Fasth vaulted by him.
'I got the putter working better today which made all the difference,' said Tunnicliff, a two-time winner on the European Tour.
Steven Bowditch, who held the lead after the opening round, started on the back side with a birdie at the 10th, but soon found trouble with a bogey at the 13th and a double bogey at the par-4 16th.
The Australian countered on the front nine with a birdie at the first and an eagle at the second. He struggled with two straight bogeys from the third, but recovered with three consecutive birdies starting at the par-4 fifth.
Bowditch then birdied the par-4 ninth to complete a 69. The 21-year-old was joined by Richard Green, Robert Karlsson, Jose Manuel Lara, Damien McGrane, Garry Houston and Rolf Muntz at 11-under-par 133.
The cut fell at 4-under-par 140 with 79 players qualifying for the weekend. Among those who failed to make the grade was Kiwi favorite Michael Campbell.