Englishman Brown grabs Open lead as McIlroy and Woods struggle
Brown, the world number 272, birdied two of the last three holes to lead by one from 2019 winner Shane Lowry.
"I'm going to try and sort of keep my feet on the ground a bit and take on the job again tomorrow," said Brown, who is competing at his first major.
McIlroy posted a seven over par round of 78 with his hopes of ending a 10-year wait to win a major floundering as most of the field struggled in the wet and windy conditions on Scotland's west coast.
Of the 156 players in the field to complete their rounds, only 17 posted a score under par.
Lowry, who won his sole major at the British Open five years ago, made the most of the calm late afternoon conditions with three birdies in five holes around the turn and picked up another at the 18th.
"I'd give anything to win this tournament again," said Lowry.
"It's great, but there's three rounds left. If I don't play well the next three rounds, it doesn't matter what I shot today. I'm fully aware that I have a job to do over the next three days."
Two-time major winner Justin Thomas is lurking at three under, while recently crowned USPGA Championship winner Xander Schauffele is among a group of seven on two under that also includes Justin Rose.
World number one Scottie Scheffler cut a frustrated figure on the greens but is still in the mix after a one under round that featured four birdies and three bogeys.
McIlroy was aiming to get over his heartbreak at the US Open last month, where he missed two short putts to blow the lead as Bryson DeChambeau claimed his second major by one shot.
However, the Northern Irishman's round, and probably championship, was blown off course at the postage stamp 120-yard eighth.
McIlroy was unfortunate as his near-perfect tee shot slipped off the green into a bunker, which he took two attempts to escape, to post a double bogey five.
Another double bogey followed at the 11th. He also dropped shots at the 10th, 15th and 18th.
"All I need to focus on is tomorrow and try to make the cut," said McIlroy.
"I need to go out there and play better and try to shoot something under par and at least be here for the weekend, if not try to put myself up the leaderboard a bit more and feel like I have half a chance."
Woods wobbles
DeChambeau had been the form player in the majors so far this year, despite his defection to the breakaway LIV Tour.
The American finished sixth at the Masters and runner-up in the USPGA Championship before claiming his second US Open.
However, his struggles with the windy conditions of links golf continued as he was six over par for his opening nine holes.
DeChambeau battled back on the back nine as an eagle on the 17th helped him to a 76.
"I'm just proud of the way I persevered today," said DeChambeau.
"I could have thrown in the towel after nine and could have been like, 'I'm going home'. But no, I've got a chance tomorrow. I'm excited for the challenge."
Thomas recovered from his own double bogey at the 12th to post a 68, which was 14 shots better than his opening round at Royal Liverpool 12 months ago.
World number three Schauffele continued his fine form in recent months as he dropped just one shot to put himself among the chasing pack.
Tiger Woods had hit back at suggestions from former European Ryder Cup captain Colin Montgomerie that he should retire, but the 15-time major champion failed to prove he can still be competitive with a 79.
"I didn't do a whole lot of things right today," said Woods. "I had three 3-putts today. I didn't hit my irons very close, and I didn't give myself a whole lot of looks today."
Cameron Smith, champion at St. Andrews two years ago, fared even worse with an 80.
World number four Ludvig Aberg was another of the big names to falter in his first ever round at a British Open with a four-over round of 75.