Fisher missed that but completed his par to write his name in the European Tour record books.
He bagged 10 birdies and an eagle without a single dropped shot as he soared to the top of the leaderboard, where he was joined by compatriot Eddie Pepperell and Australian Lucas Herbert in a three-way tie for first place ahead of the weekend.
Another Englishman, Matt Wallace, was a shot further behind on 11-under.
Sergio Garcia stayed on track to continue his warm-up for next week's Ryder Cup with second round 70 that allowed the Spaniard to make the cut for the weekend despite ending his round with three consecutive bogeys.
Since the formation of the European Tour in 1972 there have been 19 rounds of 60.
"It feels great," said Fisher, whose opening round on the Dom Pedro Victoria Golf Course, was a pedestrian level-par 71.
"I started off with three straight birdies and then kept it going. I'm just pleased that I two-putted there from 40-foot on the last. It was a great day.
"It was fun, I tried to enjoy it and thankfully I got over the line."
London-based Fisher's previous claim to fame on the European Tour was winning the Czech Open in 2011 -- his only title.
While not unheard of, sub-60 rounds are extremely rare in professional golf.
Al Geiberger was the first player to do it on the PGA Tour with a 13-under 59 at the Memphis Classic in 1977, while Chip Beck also carded a 59 at the Las Vegas International in 1991.
Since David Duval also managed a 59 at the Bob Hope Classic 19 years ago there have been five more 59s and a PGA record 58 put together by 2018 U.S. Ryder Cup captain Jim Furyk.
Furyk, who also has a 59 to his name, carded his 58 in 2016 at the Travelers Championship.
American Brandt Snedeker scored a 59 this year on the PGA Tour at the Wyndham Championship.
(Reporting by Martyn Herman in London, Simon Jennings in Bengaluru; Editing by Hugh Lawson, Toby Davis and Pritha Sarkar)
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