The Spaniard joined England's Nick Doherty and Sweden's Peter Hanson by making pars on the final four holes.
"It's been a long while since I've had a round with no bogeys," Doherty said while watching Linhart from the clubhouse. "I've not played a good round in what feels like forever, but I played some really great golf out there."
Linhart's round included seven birdies and three bogeys, while Hanson closed with a bogey at 18 which cost him the outright overnight lead.
England's Peter Baker and Paul Broadhurst joined five others at 3-under 67, good for fourth place.
Finland's Mikko Ilonen, a two-stroke winner last season, opened with an even-par 70 to join a group of 17 golfers in 34th place.