Watson determined in Augusta
Watson carded a second-round 68 in testing conditions at Augusta National to set the clubhouse target on seven under par, four shots ahead of Bjorn, who had been a total of 51 over par in 10 previous Masters appearances before this week.
"This year I'm trying to get the (green) jacket back," said Watson, who had five birdies in a row from the 12th before a bogey on the 18th, only his second dropped shot of the week. "You want that feeling again, you want that back.
"You are not the main man, the champions' dinner is not about you. Somehow I was lost in the crowd a little so I could go about my practice rounds without much attention."
Watson was the only player in the 97-strong field to card a bogey-free opening round and although the flamboyant left-hander finally dropped a shot on the ninth on Friday, birdies on the seventh, 12th, 13th, 14th, 15th and 16th took the 2012 champion clear of the chasing pack.
But he did claim his first PGA Tour title since the Masters in February, shooting back-to-back bogey-free rounds of 64 to win the Northern Trust Open.
Overnight leader Bill Haas was four under par after eight holes of his second round, but with the wind strengthening for the later starters, Bjorn was delighted to be safely in the clubhouse on three under.
"Absolutely," said the 43-year-old Dane, who recorded four bogeys and eight birdies, four of them coming in the last five holes. "I'm going to hit some balls for 20 minutes and then go home and put my feet up.
"It was a good day. I played well all the way through and felt comfortable on the golf course today. I hit two great shots into 13 and walked off with a par and after that decided I needed to be more aggressive.
"I took the shots on at 14 and 16 and they paid off and it was nice to walk up and tap it in for a birdie on 18."
Scotland's Stephen Gallacher was also delighted with his second round, a 72 leaving him one under and guaranteed to make the halfway cut on his Masters debut - something his uncle Bernard, the former Ryder Cup captain, was unable to do in 1970.
"I'm delighted to still be in red numbers to be honest," Gallacher said. "It was a bit tricky, the wind is a bit up and the greens are firming up.
"It's a very strategic course. I think everybody back home knows how to play it, it's just a case of trying to do it that's the hard part."
Former Open champion Louis Oosthuizen, who lost a play-off to Watson in 2012, held a share of the lead when he holed from five feet for an eagle on the 13th.
But the South African then ran up a triple-bogey eight on the 15th after chipping from the back of the green into the water at the front, before a bogey on the 18th meant a round of 75 and left him level par for the tournament.
Three-time Masters champion Phil Mickelson was in danger of a first missed cut since 1997 after a triple-bogey on the 12th contributed to a 73 and left him five over par. But playing partner Justin Rose, who was six over par after 12 holes on Thursday, bounced back from an opening 76 with a round of 70 to lie two over.
The top 50 players and those tied for 50th will make the cut, along with anyone within 10 shots of the lead.
Defending champion Adam Scott had matched Watson's opening 69 but got off to a poor start to his second round, dropping shots at the first, fourth and fifth to drop back to level par.
And things could have been worse for the world number two, who was almost hit by a wayward tee shot from Rory McIlroy as he stood on the fifth tee.
McIlroy had recovered from a bogey on the second with a birdie on the third, but hit his tee shot on the fourth way over the green, the ball bounding just past Scott and into an unplayable lie in the bushes.
After contemplating taking a penalty drop, McIlroy opted to go back to the tee and eventually completed a double-bogey five before bouncing back with a birdie on the next.
Welshman Jamie Donaldson was proving good scoring was still possible however, birdies at the second, eighth and ninth taking him into the top 10 on two under.
Australia's John Senden completed a fine 68 to move within three shots of Watson's lead, but McIlroy's struggles continued with a double-bogey on the 10th - where he took seven in his final-round collapse in 2011 - and a bogey at the 11th.
With a birdie chance going begging on the 12th, McIlroy remained three over and more worried about making the cut than catching the leaders, while Scott did birdie the 12th in the group ahead to get back under par.