World number one Tiger Woods lurked three strokes back, with the opening event of the FedExCup playoffs stalled for more than six hours by heavy lightning and two rain delays.
Some 63 players, including British Open winner Phil Mickelson and Masters champion Adam Scott, were unable to complete their rounds and face an early start on Friday and another long day.
The 33-year-old Stadler, winless on the PGA Tour, made the most of his chances, however, registering seven birdies in a bogey-free round at Liberty National where bright sunshine eventually replaced the dark, stormy skies across the harbor from downtown Manhattan.
Tied for second on six-under were Sweden's Henrik Stenson, Colombia's Camilo Villegas and American Ryan Palmer, with Australian Jason Day and another American in Matt Kuchar a further shot adrift.
Woods, who began his long day at the 10th hole, reached four-under by adding a birdie at the par-three fourth after his run of three straight birdies was interrupted by the second weather delay.
The playoffs points leader, who has already won five tournaments this season, parred his last five holes for 67 and was satisfied after a gruelling day.
"I'm actually tired," Woods told reporters. "I got up at four this morning and I think it took us, from start to finish just under 11 hours for the day. Long day.
"I'm only three back. We have a long way to go."
Stadler was thrilled with his showing given his lacklustre season, the American posting just two top-10 finishes with a tie for third at Pebble Beach his best result.
"I've had kind of a pretty lousy summer, result-wise," said Stadler, the son of 13-time PGA tour winner Craig Stadler.
"But I really started hitting the ball a lot better a couple of weeks ago.
"Felt like I was heading in the right direction even though the results were not showing it and finally got something out of it today."
In contrast, Stenson has been on a roll. Runner-up at the British Open, tied for second at the WGC-Bridgestone and third at the PGA Championship in his last three events, the 37-year-old Swede continued his impressive form at Liberty National.
Stenson made nine birdies along with three bogeys, the last of which came on his penultimate hole and dropped him from a share of the lead.
"To be honest, I came in from Europe on Monday night, so I'm a bit jet-lagged and I only saw the course once," said Stenson. "I'm very pleased with the way I played out there."
Villegas shot to eight-under when he posted his fourth birdie in a row at the par-three 11th, but back-to-back bogeys from the 14th saw him ease off the pace.
"Three breakfasts, three warm-ups, two lunches and a bunch of birdies which is good," said Villegas, describing his day.
Among the late starters, American Harris English was four- under through six holes and Australian Marc Leishman was three-under through eight.
Americans Webb Simpson and Bubba Watson, who had both played six holes, were among a large group at two-under par.
Mickelson was one-under after six, one stroke better than Scott, who had also played six holes by the time the horn sounded due to darkness.
The late finishers can expect an arduous test on Friday when they finish the first round and head right out for the second round.
Thursday's early starters will get their second rounds started later on Friday and will have to complete them on Saturday morning.