Hendrik Buhrmann, Jamie Donaldson, Jean-Francois Remesy, Nic Henning, James Kingston, Greg Owen and Mark Roe are tied for third at 5-under-par 67.
Ernie Els and Retief Goosen, two South Africans with three U.S. Open titles between them, are part of a logjam in 10th at 4-under par.
'I played reasonably well and had quite a few birdie chances but didn't play the par-5s that well,' said Els, referring to his 68 on Thursday. 'I can't say I'm over satisfied with my opening round but at least it's under 70 and it's 4-under par.'
McGinley picked up three birdies on his first nine, the back nine at Houghton Golf Club, but he climbed up the leaderboard late in his round. He birdied the par-5 5th and hit the stick with his tee shot at eight. The near ace set up birdie and he closed his round with a birdie at the 471-yard 9th.
'I'm surprised but pleased,' said McGinley. 'I've just had six weeks off but often it's good to be fresh. I scored well today without playing particularly well. But you can't shoot 66 around here and play poorly. Overall I'm very pleased.'
The Irishman did not intend to compete in this tournament because he wanted to play in more events in America. However, the sponsor's exemptions were not rolling in as he thought they might.
'I had intended going to the West Coast but didnt get enough invitations to make it worthwhile,' said McGinley, who is ranked 32nd in the world and will make his Ryder Cup debut in September. 'It was disappointing, but its not an issue for me to raise.'
Dodd started on the second nine as well and parred the first five holes but went 4-under over his next four to make the turn in 32. He added birdies at Nos. 3 and 5 for his flawless 66.
The 35-year-old finished 66th last week at the South African Open but the end result could have been better. He posted 19 birdies and an eagle in the tournament but that was negated by 14 bogeys, three double-bogeys and a quadruple-bogey.
'Last week I made loads and loads of birdies but quite a few mistakes as well. Today I made the birdies and didn't make the mistakes. I just went out and played and tried my best,' Dodd said.
Andrew Coltart, Carl Pettersson, Mark Pilkington, Mark Mouland, Alastair Forsyth, Anthony Wall, Roger Wessels and Marc Cayeux joined Els and Goosen at 4-under.
Former professional soccer player Roy Wegerle made his professional golf debut on Thursday and it got off to a great start with a birdie at the first hole. It went downhill from there as Wegerle finished with a 4-over 76.
'I was nervous out there, but that's natural,' Wegerle said. 'I played nicely, but I made a few silly mistakes. For instance, I was able to reach all of the par-5s in two, but couldn't take advantage of that.'
Paul Lawrie, the 1999 British Open champion, withdrew from the tournament before play began on Thursday. The Scotsman suffered a back injury and felt unable to compete.
Full-Field Scores from the Dunhill Championship