McDowell's 62 matched the total put up by Brian Davis in 2003. McDowell had carded a 62 at the BMW International Open earlier this year, but that came under preferred lies.
Retief Goosen, the reigning U.S. Open champion, Peter Lonard, David Howell and James Kingston share second place at 7-under-par 65.
The top two players in the world, Vijay Singh and Ernie Els, both stand at 4-under-par 68. They were joined there by Thomas Levet, Colin Montgomerie, Jose Maria Olazabal, Adam Scott and Peter Hedblom.
The tournament is using three courses as it has a pro-am competition for the first three rounds. McDowell played the Old Course at St. Andrews, while others played at Carnoustie Golf Club and Kingsbarns Golf Links. Players will rotate over the three courses for the first three rounds, before the final round is contested at St. Andrews.
McDowell got on the board with a birdie at the par-4 third. He picked up his second birdie at the fifth. The 25-year-old came back with a birdie at six and made it three in a row when he drained a birdie at the seventh.
The Ulsterman closed his opening nine with a birdie at the ninth to go out in 5 under. McDowell caught fire early on the back side as he converted a birdie at the 11th and made it two in a row at 12.
McDowell rolled in a 15-foot birdie try at the 13th to get to 8 under. He two-putted for birdie from just off the front edge of the green at the par-5 14th to cap a run of four straight birdies.
McDowell, who won the Italian Open earlier this year, parred his next two holes. He then dropped a 7-iron within 10 feet of the cup to set up his 10th birdie of the day at the 17th.
At the last, McDowell's birdie putt from inside 10 feet slid by the right edge and he settled for par and a share of the course record.
'I was walking up to the green with my caddie, and I said to him, 'I saw this putt a million times on television and I know exactly where it's going,'' said McDowell. 'But it turned more than I expected.
'It wasn't exactly one you want to leave yourself for a 61, but I had a great second shot in there and I gave the putt my best and didn't leave me that much of an effort at the end. But 62 strokes out there today, I'm very, very happy.'
Goosen posted a bogey-free round of his own. He birdied the second at Kingsbarns to start his round. Goosen then ran off three straight birdies from the fifth. Around the turn, he birdied the 10th and 12th to get to minus-6. After five straight pars, the South African birdied the last.
'I'm happy with that,' Goosen said. 'We were lucky with the wind dying down a little bit on the back nine because the course is tough. I got off to a good start with a birdie on the second hole. That settled me down and then I had a good run of three birdies in a row from the fifth.'
Howell, who also played Kingsbarns, ran off three straight birdies from the first to start his round. He later birdied Nos. 6 and 9 to make the turn at 5 under. He picked up two more birdies on his way in to share second place.
Lonard also picked up five birdies over the front nine at Kingsbarns. On the back side, the Australian birdied two of his last three holes to end at minus-7.
Kingston, the final player three shots back, played Carnoustie in Round 1. After birdies at one and three, he stumbled to a bogey at the sixth. Kingston responded with birdies on each of the next two holes to make the turn at 3 under.
Kingston eagled the par-5 12th and birdied the 15th to move to 6 under. The South African closed with a birdie at the last to join the crowd in second place.
Richard Sterne and Luke Donald share sixth place at 6-under-par 66. Gregory Havret, Louis Oosthuizen and Gordon Brand, Jr. are one stroke further back at minus-5.