Sharing second place on 214 were Norman's playing partner and overnight leader KJ Choi of South Korea (75) and champion Padraig Harrington (72).
One stroke further adrift was British journeyman Simon Wakefield, who equalled the day's best round with a level-par 70.
In joint fifth spot on 217 were Americans Ben Curtis and Anthony Kim, Briton Ross Fisher and Alexander Noren of Sweden.
"I'd put that in the top three hardest rounds I have ever played under those circumstances," Norman said.
"The wind was so heavy and so strong, it was just brutal."
Norman, known as the Great White Shark in his heyday, married tennis great Chris Evert last month.
He hardly hit a fairway on Saturday but kept errors to a minimum.
With Evert standing by the 18th green, he drew gasps from the crowd when a tricky chip from behind a bunker narrowly missed the cup.
Asked what it would mean to win a third major title, Norman said: "I'm not going to get ahead of myself. Ask me that question tomorrow night."
Earlier, he bogeyed three of the first six holes but got back in gear by holing a 10-foot birdie putt at the eighth.
Norman, who only committed to playing here two months ago, stalled with a double-bogey six at the 10th before gathering further birdies at the 14th and 17th.
"I'm going to keep the same [relaxed] mindset," he said.
"I have the lead now and it's going to be tough again tomorrow.
"I walked to the first tee nervous today and that was a good indicator for me. I haven't felt that way for 10 years."
With trousers billowing in the sunshine, flags bending at 90-degree angles and baseball caps flying across the Royal Birkdale links course, birdies were scarce.
Scores soared and the 83-strong field took a battering on one of the most difficult days for golf in the 137th edition of the game's oldest championship.
Organisers tried to soften the blow by moving the tees forward, but it did nothing to help former world number one David Duval, who had a torrid time as he plunged to an 83.
The exposed 408-yard, par-four 10th caused no end of problems, moving balls on the green prompting frequent delays.
Norman and Choi were involved in one logjam which sparked a 25-minute wait on that tee.
Harrington, without a European Tour victory since he captured the prized Claret Jug at Carnoustie 12 months ago, boosted his hopes with four birdies.
The 36-year-old Irishman broke into a trademark grin after snapping up birdie fours at the 15th and 17th.
"I look forward to the challenge tomorrow," Harrington said.
"More high winds would probably give me my best chance of winning."
Asked about the wrist injury he suffered prior to the event, Harrington replied: "Good for me I only played nine holes before the tournament or the 54 holes would probably feel like 108".
One of the day's best displays came from 2003 champion Curtis, who returned a 70 as the white-horse waves reared up in the distant Irish Sea.
He defied the elements with a magical outward half of 31 containing two birdies and an eagle two, the American holing his 165-yard, nine-iron approach on the par-four third.