Fasth was joined atop the leaderboard by Ireland's Gary Murphy and South African Andrew McLardy.
Argentine Ricardo Gonzalez shot a 2-under-par 68. He stands alongside three Englishmen -- Jonathan Lomas, Phillip Archer and Tom Whitehouse -- in a tie for fourth.
The first three years of this event, the winner has been a native Spaniard. Jose Manuel Lara posted a 1-under-par 69 and shares eighth place. He was the low Spaniard of the round. Sergio Garcia is next at even-par 70.
Fasth, like his fellow co-leaders, started on the 10th tee at Pula Golf Club on Thursday. Fasth was steady over the back nine, carding a lone birdie on the par-4 16th. He parred the other eight holes of his opening nine.
The Swede moved to minus-2 with a birdie on the par-4 first. Fasth followed a birdie on the par-4 fourth with birdies on five and six to climb to 5 under. He bogeyed the ninth, his last, when he failed to get up and down from a bunker.
'It was not brilliant, but steady,' Fasth admitted. 'I thought more would happen after the Spanish Open, but I just made cuts which has been a bit frustrating. Today I was happy with the round.'
Murphy got off to a quick start with birdies on 10 and 11. He got to minus- three with a 25-foot birdie putt on the 14th, but a bogey on 17 dropped him back to 2 under around the turn.
The 34-year-old Irishman birdied the first, but gave another stroke back with a three-putt bogey at the third. Murphy got back to minus-3 as he birdied No. 5 and a birdie on the par-3 eighth gave him a piece of the lead.
'You try not to dwell on your situation, but it's not to be confused with enjoyable,' said Murphy, who clings to the 118th and final spot for retaining his tour card for next season. 'I probably concentrated a little better today and maybe that's what I've not been doing enough this year.'
McLardy was 1 under through nine holes thanks to a pair of birdies and a bogey on 14. He moved to minus-2 when he birdied the first. The South African fell back to even-par after a double-bogey 6 on the third.
He quickly rebounded with a birdie at the fourth. McLardy made it two straight as he converted a birdie effort at five. He made it three in a row with a birdie on six and climbed to minus-4 as he birdied the par-3 eighth.
Lara is tied for eighth place with Peter Fowler, Christian L. Nilsson and David Park.
Padraig Harrington, second in the Order of Merit, and Robert Karlsson, fourth, each have a chance at catching Paul Casey for the lead in the Order of Merit.
Karlsson is tied for 23rd at plus-1, while Harrington had a much tougher day. The Irishman, who would pass Casey for the Order of Merit lead with a win this week, struggled to a 7-over-par 77. He is tied for 90th.
'I didn't inspire myself with my ball-striking, but I'll go out and try tomorrow,' said Harrington, who triple-bogeyed the 16th after hitting out of bounds and taking an unplayable lie. 'A change of wind direction from what I practiced in put a little bit of doubt in my head and I made a lot of uncommitted swings.'