Fasth and Murphy, who stand atop the leaderboard at 3-under-par 137, shared the lead after the opening round with Andrew McLardy.
Marc Warren is alone in third place at minus-2 thanks to a 2-under 68 Friday. Diego Borrego leads the Spanish contingent at 1-under-par 139. He also shot 68 Friday at Pula Golf Club to move into fourth.
Spain's Alfredo Garcia-Heredia also posted a 68. He stands at even-par 140 and was joined there by countryman Sergio Garcia, Andrew Marshall, Peter O'Malley and Soren Kjeldsen.
With the wind swirling for the second straight day, scores soared again as just nine players broke par. All nine of those scores were either 68s or 69s.
Fasth stumbled out of the gate as he dropped shots on the second and fourth. He rebounded to birdie No. 5 for the second straight day, but gave another stroke right back at the sixth.
The Swede fought back with birdies on seven and eight to get back to even-par for his round and minus-four overall. Fasth tripped to a bogey on 10, then ran off eight straight pars to close out his round and tie Murphy for the lead.
'It was extremely tough out there and the wind was constant pretty much all of the day, it didn't really start dying until we had about two or three holes to go,' said Fasth, who won the Andalucia Open earlier this year. 'It is hard going, but if you keep playing well you can get it round. I am playing well just now, but I holed really nothing today.'
Murphy, who was in the first group out in the afternoon wave of tee times, bogeyed the first. He got that shot back with a birdie on two, but then bogeyed the third.
The Irishman birdied the fifth for the second day in a row. Murphy faltered to a bogey on seven then parred his next five holes. He slid to minus-2 after a bogey on 13, but rebounded with a birdie at the 14th before closing with four pars.
Murphy entered this event ranked 118th on the Order of Merit. That is the final spot for those who will retain their playing privileges for next year.
'Maybe I need a little bit of stress to get the best out of myself and play a bit better,' Murphy admitted. 'I'm pleased with myself up to here, but it is still not going to be an easy weekend. We are still only halfway there and I can't rest on my laurels. Pars are your friends out here because the conditions are so tough.'
Steven Jeppesen, Jose Manuel Lara, Jonathan Lomas, Benn Barham and Peter Hanson share 10th place at 1-over-par 141.
Robert Karlsson, who has a chance to overtake Paul Casey in the Order of Merit race, stands at plus-2 after back-to-back 71s. He is tied for 15th with McLardy, who struggled to a 6-over 76.
The cut line fell at 8-over-par 148 with 76 players moving on to the weekend. Among those who missed out on the weekend were 2005 champion Jose Maria Olazabal and Padraig Harrington.
Olazabal, who redesigned Pula Golf Club, shot 78-72 to end at 10-over-par 150. This was the Spaniard's first missed cut of the season on the European Tour.
Harrington, who could also pass Casey for the top spot on the Order of Merit, posted 77-74 to finish at plus-11. Harrington will have to finish no worse than solo third next week in order to have a chance at passing Casey.
'That's golf, it sometimes goes like that,' Harrington said. 'It was difficult conditions out there and it was a course you wanted to be ahead of rather than trying to attack it. I just left myself too much to do.'