Zoeller and Streck both carded eight birdies with one bogey at the 7,069-yard TPC of Michigan, where 58 players in a field of 78 were even par or better after the first day.
Jim Thorpe and Scott Simpson completed bogey-free rounds of 5-under 67 and share third place with Bruce Lietzke.
Jay Haas and Allen Doyle -- winners of the year's first two majors -- are one shot further back in a group that also includes Tom Jenkins, Brad Bryant, John Jacobs and Tom Kite at minus-4.
Fred Funk ruined a perfect drive at the par-5 17th by knocking his second shot into the water on the way to a bogey. He finished at 3-under 69 and leads 14 players who are tied for 12th.
Funk, 50, made his Champions Tour debut last week at the U.S. Senior Open and finished tied for 11th place.
The TPC of Michigan greens are small and undulating, but conditions were ripe for scoring Thursday.
Streck started out with a poor chip shot and a bogey at the first hole, but went 8 under par the rest of the way. He birdied the third, seventh and ninth holes on the front nine -- all on putts inside 10 feet -- then collected five consecutive birdies beginning at the 13th.
'It was a good day after the start,' Streck said.
At the par-4 16th, Streck rolled in a 21-foot birdie putt. Two holes later, he saved par from a bunker at 18 by draining a 13-footer.
'I just didn't want to ruin the round on the last hole,' Streck said. 'I looked at it and thought, 'Don't mess this up by bogeying the last hole.' So I was lucky to make that.'
Streck owns a share of the first-round lead six days after missing the cut at the Senior U.S. Open following rounds of 72 and 77 at Prairie Dunes. He spent some time at home after that.
'I went home and put siding on my garage on Saturday and Sunday,' he said.
Zoeller birdied the second, third and fifth holes Thursday to make the turn at minus-3. He birdied three holes during a four-hole stretch beginning at the 10th -- including one on a 36-foot putt at the par-three 12th -- then stumbled to his only bogey of the round when he missed a 3-foot putt at the par-4 16th.
Two straight birdies to end his round placed Zoeller in a first-place tie with Streck. He finished his round with a 13-foot birdie putt at the par-4 18th.
'I played very well today,' said Zoeller, who tied for 23rd last week. 'Did I see it coming? Kind of. It's a golf course I enjoy playing. I have a good feel for it.'
This is the second of three straight majors on the Champions Tour and third overall this season. Haas won the Senior PGA Championship and Doyle edged Tom Watson last week at Prairie Dunes.
Watson, who will defend his Senior British Open title in two weeks, is one of the players tied for 12th place with Funk at minus-3.
Defending champion Peter Jacobsen opened with a 2-under 70 and is tied for 26th place.