The Spaniard led overnight after an opening 64, but a three-putt bogey on the 12th and a double-bogey seven on 13 means he is tied second on nine under par with Thailand's Thongchai Jaidee.
Bjerregaard's six-under-par 66 included seven birdies and one bogey.
Englishmen Ian Poulter and Paul Casey are tied fourth on eight under.
Poulter's score came after a second consecutive round of 68, finishing with four birdies in the last six holes after a mixed card until that point.
Casey dropped a shot on the 12th in an otherwise flawless 69, which included four birdies.
"It was a great round and obviously finished off with some good birdies coming in," said Bjerregaard, who covered the back nine in 35 after starting from the 10th and birdied five of his last eight holes to come home in 31.
"Nothing much really happened on the first nine, I just played really solid. But I thought it was a good bit tougher than [Thursday] with the wind up. Some of the holes were playing really long."
England's Ross Fisher, who lost out in a three-man play-off last year, was in contention to join the leaders after five birdies and a bogey on his first 13 holes.
But further dropped shots on 14, 15 and 18 meant he slipped to seven under, five shots off the lead.
Sergio Garcia is three shots behind new BMW Masters leader Lucas Bjerregaard from Denmark after carding a one-under-par 71 in the second round.