'I just was really calm today. I felt good,' said Inkster. 'I felt like I was playing well enough to go out there and shoot a good score. I was just kind of focusing on what I needed to do and just get the ball on the green and get an opportunity for birdie.'
Lorie Kane was four shots back in second place at 20-under-par 268. She was followed by overnight leader Catriona Matthew at 19-under-par 269.
Inkster, who made her first appearance at Corning since 1996, rocketed out of the gate to start her record final round. After a par at the first, she birdied the second and hit her tee shot to 12 feet for a birdie at the par-3 third.
Inkster landed her approach within three feet for a birdie at the fourth and made it four in a row with a birdie at the fifth to surge to the top of the leaderboard.
She added back-to-back birdies starting at the seventh to go out in 30 and notched the first of three consecutive birdies from the 10th to move to 23-under.
With six holes remaining, Inkster had the magical mark of 59 in sight but the veteran had to scramble down the stretch until trouble found her at the 16th.
Inkster was in the rough at the par-4 hole and her third shot fell short of the putting surface. She nearly saved par from off the green when her ball bounced off the cup but the end result was a crucial 10-foot bogey putt that remained.
The 42-year-old made the putt to fall back to 22-under as Kane began to close in. Inkster recovered almost instantaneously at the par-4 17th when her second shot from a fairway bunker stopped four feet from the hole for a birdie.
At the 18th, Inkster hit her approach to 20 feet and capped her first victory since the 2002 U.S. Women's Open in fine fashion, draining the birdie putt to establish a new course record at Corning Country Club.
'It's great to have those records, but some day they'll be broken,' said Inkster, whose 62 was the lowest final round by a winner in LPGA Tour history. 'But you'll always be a winner here, which is great.'
Kane battled throughout the round to keep pace with Inkster. She had a hot start with four birdies over her first nine holes but could not keep up with the eventual champion on the inward half.
The Canadian birdied the par-5 12th to reach 20-under and parred in for her second runner-up finish of the season.
'I made some good saves, but I didn't get it done coming down the stretch, simple as that, with Juli ahead of me, knowing what she was doing,' said Kane. 'It's been a very positive week, to play the weekend with no bogeys is something that I'm going to carry with me for the rest of the season, I hope, and build from there.'
Meg Mallon and Beth Daniel each carded rounds of 68 to finish tied for fourth at 18-under-par 270.
Rosie Jones, who won this event in back-to-back seasons starting in 1996, was two shots further back along with Anna Acker-Macosko and Soo-Yun Kang at 16- under-par 272.
Last year's winner Laura Diaz made a splash early with a 9-under 63. She finished 12 shots off the lead at 12-under-par 276.