The 46-year-old American's 12-under round bettered the previous record of 59 which had been shot six times, including by Furyk himself.
"There are a lot of rounds by a lot of great players ahead of me that have never reached 58. So to hold it on the PGA Tour is phenomenal," Furyk said.
Furyk two-putted on the 18th green after setting the nine-hole record with an eight-under 27. He shot a 31 on the back nine in his closing round.
Scotland's Russell Knox sank a 12-foot putt on his closing hole to shoot a two-under 68 and earn his second tournament victory of the season. Knox finished one stroke ahead of first round co-leader Jerry Kelly, who shot 64.
Furyk, who finished tied for fifth, described his closing round as a grinding, mental struggle.
"I am hitting it well. I am putting it well. It is trying to find a way to stay out of your own way, really. Don't let any (negative) thoughts in," he said.
A birdie at the 12th hole was his seventh straight and he finished with a two-foot par putt on 18 at the River Highlands course in Cromwell, Connecticut.
Two other professionals have recorded 58s, comprising Germany's Stephan Jaeger on the Web.Com Tour in this year's Ellie Mae Classic and Japan's Ryo Ishikawa on the Japan Golf Tour at the 2010 The Crowns.
Furyk began the day 16 shots back of leader Daniel Berger in 70th place at one-over 211 after opening 73-66-71. He finished at 11-under 269.
It was one shot off the PGA Tour's nine-hole record of 26, set by Corey Pavin in the opening round of the 2006 US Bank Championship in Milwaukee.
- Front nine premonition -
==========================
Furyk said he realized he could accomplish something historic when he was still on the front nine.
"Late on the front nine, I felt good with my short irons. I had a special feeling.
Furyk, who is ranked 24th in the world, won the 2003 US Open and is a 17-time winner on the US PGA Tour. He last won at the 2015 RBC Heritage.
Fellow golfer Graeme McDowell said he has great respect for Furyk.
"Special round of golf there from Furyk," McDowell tweeted. "Cool to see how emotional he was. Golf is hard and days like that don't happen often. #58."
American Chris DiMarco is amazed Furyk has gone so low twice.
"Wow. Congrats to Jim Furyk. What a round of golf. First to shoot 58 on tour and becomes first man to shoot in 50's twice!," DiMarco tweeted.
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