The 33-year-old Swede, who made his major debut at the PGA Championship this spring, got off to a dream start on the first day, with three birdies and an eagle on the front nine. Lindberg then faded a little but bounced back with two more birdies to finish at -3.
Superstar Ludvig Åberg shot an even-par round.
The Open de España is part of the DP World Tour, formerly known as the European Tour. The tournament runs until Sunday.
